The maximum value of function x^3 - 12 x^2 + 36x + 17 in the inte… - Vidyadip

MCQ

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

A
$17$
✓
$177$
C
$77$
D
None of these

✓

Answer

Correct option: B.

$177$

b
(b) Let $f(x) = {x^3} - 12{x^2} + 36x + 17$

$\therefore f'(x) = 3{x^2} - 24x + 36 = 0$ at $x = 2,\,6$

Again $f''(x) = 6x - 24$ is $ - ve$ 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 as $ 177.$

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