Consider the function \(f(x)=\frac{x^3}{3}+\frac{7}{2}x^2+10x+\frac{133}{2}\),…

GATE · 2025 · DA · Data Science & AI

Consider the function $f(x)=\frac{x^3}{3}+\frac{7}{2}x^2+10x+\frac{133}{2}$ , $x\in[-8,0]$ . Which of the following statements is/are correct?

A.
The maximum value of f is attained at x = −5
B.
The minimum value of f is attained at x = −2
C.
The maximum value of f is $\frac{133}{2}$
D.
The minimum value of the derivative of f is attained at $x=-\frac{7}{2}$

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