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Application Of Derivatives

Question

Wired Faculty App

Find the intervals in which the function f(x) = $\frac{x^{4}}{4} - x^{3} - 5 x^{2} + 24 x + 12$ is
a) Strictly increasing
b) Strictly decreasing

Solution

f'(x) = x³ -3x² - 10 x +24

f'(x) = (x+ 3)(x-2)(x-4)

f(x) is strictly increasing

if f'(x)>0

$∴ x \in (- 3, 2) \cup (4, \infty) f (x) is strictly decreasing if f' (x) < 0 ∴ x \in (- \infty, - 3) \cup (2, 4)$

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