The maximum value of 2 x^3 - 24x + 107 in the interval [-3, 3] is - Vidyadip

MCQ

The maximum value of $2{x^3} - 24x + 107$ in the interval $[-3, 3]$ is

A
$75$
B
$89$
C
$125$
✓
$139$

✓

Answer

Correct option: D.

$139$

d
(d) Let $f(x) = 2{x^3} - 24x + 107$

At $x = - 3,\;f( - 3) = 2{( - 3)^3} - 24( - 3) + 107 = 125$

At $x = 3,\;\;f(3) = 2{(3)^3} - 24(3) + 107 = 89$

For maxima or minima, $f'\,(x) = 6{x^2} - 24 = 0$

$ \Rightarrow x = 2,\;\; - 2$

So at $x = 2,\;f(2) = 2{(2)^3} - 24(2) + 107 = 75$

at $x = - 2,\;\;f( - 2) = 2{( - 2)^3} - 24( - 2) + 107 = 139$

Thus the maximum value of the given function in $ [-3, 3]$ is $139.$

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