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AP EAMCET · Maths · Application of Derivatives

If \(\mathrm{A}=\left\{\mathrm{x} / 9 \mathrm{x} \geq \mathrm{x}^2+20\right\}\) and \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}\) is defined by \(f(x)=2 x^3-15 x^2+36 x-48\), then the maximum value of \(f(x)\) is

  1. A -20
  2. B 7
  3. C 20
  4. D -16
Verified Solution

Answer & Solution

Correct Answer

(B) 7

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & \text { Given } \mathrm{A}=\left\{x: 9 \mathrm{x} \geq \mathrm{x}^2+20\right\} \\ & \mathrm{A}=\{x: x \in[4,5]\}=[4,5] \\ & \text { Given } f(x)=2 x^3-15 x^2+36 x-48 \\ & f^{\prime}(x)=6\left(x^2-5 x+6\right)=6(x-3)(x-2) \end{aligned} \] For maxima or minima…