Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing.
f(x) = 2x² - 24x + 7

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Answer

We have
f(x) = 2x² - 24x + 7
f'(x) = 6x²- 24
Critical points
f'(x) = 0
⇒ 6x²- 24 = 0
⇒ 6x²= 24
⇒ x² = 4
⇒ x = 2, -2
Clearly, f'(x) > 0 if x > -1 and x < -2
f'(x) < 0 if $-2\leq\text{x}\leq2$
Thus, f(x) increasing in $(-\infty,-2)\cup(2,\infty),$ decreasing in (-2, 2).

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