Hướng dẫn giải Bài 4 (Trang 24 SGK Toán Giải tích 12)

Câu hỏi: Tính giá trị lớn nhất của các hàm số sau: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>4</mn><mrow><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo> </mo><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup></math> Hướng dẫn Giải: a) TXD: D = R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>-</mo><mn>8</mn><mi>x</mi></mrow><msup><mfenced><mrow><mn>1</mn><mo> </mo><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mn>2</mn></msup></mfrac><mo>;</mo><mo> </mo><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>⇔</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mfenced><mrow><mi>y</mi><mo> </mo><mo>=</mo><mn>4</mn></mrow></mfenced></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/18022022/anh-chup-man-hinh-2022-02-18-luc-151724-0bFiU2.png" width="584" height="90" /> Vậy max y = 4  b) TXD: D = R <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><msup><mi>x</mi><mn>3</mn></msup><mo> </mo><mo>=</mo><mo> </mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>(</mo><mn>1</mn><mo>-</mo><mi>x</mi><mo>)</mo><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><mn>0</mn><mo> </mo><mfenced><mrow><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn></mrow></mfenced></mtd></mtr><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><mn>1</mn></mrow></mfenced></mtd></mtr></mtable></math> Bảng biến thiên: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/18022022/anh-chup-man-hinh-2022-02-18-luc-151938-kCV1Ki.png" width="603" height="93" /> Vậy max y = 1