Question

The- maximum value of function $ x^3 - 12x^2 + 36x + 17 $ in the interval $ [1,10] $ is

• A. $ 17 $
• B. $ 177 $
• C. $ 77 $
• D. None of these

Answer 1

Answer: (B)

Let $f(x)=x^{3}-12 x^{2}+36 x+17$
$\therefore f'(x)=3 x^{2}-24 x+36=0$
For maxima, put $f'(x)=0$
$\Rightarrow \,\, 3 x^{2}-24 x+36=0$
$\Rightarrow \,\,\,(x-2)(x-6)=0$
$\Rightarrow \,\,\, x=2,6$
Again, $f''(x)=6 x-24$ is negative at $x=2$
So that, $f(6)=17, f(2)=49$
At the end points, $f(1)=42, f(10)=177$
So that, $f(x)$ has its maximum value $177$ .