Hướng dẫn Giải bài 1 (trang 9, SGK Giải Tích 12)

Hướng dẫn Giải Bài 1 (Trang 9, SGK Giải Tích 12)

Bài 1 (Trang 9, SGK Giải Tích 12): Xét sự đồng biến, nghịch biến của các hàm số: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><mn>7</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">c</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>4</mn></msup><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">y</mi><mo>=</mo><mo>-</mo><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo> </mo><mo>+</mo><mo> </mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><mn>5</mn><mo>.</mo></math> Hướng dẫn Giải: a) TXD: D= R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mo> </mo><mo>-</mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mspace linebreak="newline"/><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mo> </mo><mn>3</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo> </mo><mo>⇔</mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>25</mn><mn>4</mn></mfrac></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/anh-chup-man-hinh-2022-02-17-luc-225214-wov6lu.png" width="506" height="112" /> Hàm số đồng biến trên khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mo>∞</mo><mo>;</mo><mo> </mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></mfenced></math>, nghịch biến trên khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>;</mo><mo> </mo><mo>+</mo><mo>∞</mo></mrow></mfenced></math> b) TXD: D = R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo>+</mo><mn>6</mn><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>7</mn><mspace linebreak="newline"/><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mo>[</mo><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn><mo> </mo><mfenced><mrow><mi>y</mi><mo>=</mo><mo> </mo><mfrac><mrow><mo>-</mo><mn>17</mn></mrow><mn>3</mn></mfrac></mrow></mfenced></mtd></mtr><mtr><mtd><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>7</mn><mo> </mo><mfenced><mrow><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>239</mn><mn>3</mn></mfrac></mrow></mfenced></mtd></mtr></mtable></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/anh-chup-man-hinh-2022-02-17-luc-225522-AGPFbd.png" width="534" height="101" /> Hàm số đồng biến trên các khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mo>∞</mo><mo>;</mo><mo> </mo><mo>-</mo><mn>7</mn></mrow></mfenced><mo> </mo><mtext>và</mtext><mo> </mo><mfenced><mrow><mn>1</mn><mo>;</mo><mo> </mo><mo>+</mo><mo>∞</mo></mrow></mfenced></math>, nghịch biến trên khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>7</mn><mo>;</mo><mo> </mo><mn>1</mn></mrow></mfenced></math> c) TXD: D = R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo> </mo><mo>-</mo><mo> </mo><mn>4</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mi mathvariant="normal">x</mi><mo>(</mo><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn><mo>)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mo>[</mo><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mfenced><mrow><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>±</mo><mn>1</mn><mo> </mo><mfenced><mrow><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mrow></mfenced></mtd></mtr></mtable><mo> </mo><mo>⇔</mo><mo>[</mo><mtable><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mtd></mtr></mtable></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/anh-chup-man-hinh-2022-02-17-luc-225827-20anWT.png" width="566" height="107" /> Hàm số đồng biến trên các khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced><mo> </mo><mtext>và </mtext><mfenced><mrow><mn>1</mn><mo>;</mo><mo> </mo><mo>+</mo><mo>∞</mo></mrow></mfenced></math>, nghịch biến trên các khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mo>∞</mo><mo>;</mo><mo> </mo><mo>-</mo><mn>1</mn></mrow></mfenced><mo> </mo><mtext>và</mtext><mo> </mo><mfenced><mrow><mn>0</mn><mo>;</mo><mo> </mo><mn>1</mn></mrow></mfenced></math> d) TXD: D = R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mi>x</mi><mo>(</mo><mo>-</mo><mn>3</mn><mi>x</mi><mo> </mo><mo>+</mo><mn>2</mn><mo>)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mo>[</mo><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mfenced><mrow><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo>-</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo> </mo><mfenced><mrow><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><mn>131</mn><mn>27</mn></mfrac></mrow></mfenced></mtd></mtr></mtable><mo>⇔</mo><mo> </mo><mo>[</mo><mo> </mo><mtable><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><mn>131</mn><mn>27</mn></mfrac></mtd></mtr></mtable></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/anh-chup-man-hinh-2022-02-17-luc-230129-UtwpTj.png" width="552" height="137" /> Hàm số đồng biến trên khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math>, nghịch biến trên các khoảng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mo>∞</mo><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced><mo> </mo><mtext>và</mtext><mo> </mo><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>;</mo><mo> </mo><mo>+</mo><mo>∞</mo></mrow></mfenced></math>