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Popular >

extreme 24x^3-24x^2

Solution

extreme points

24 x^{3} - 24 x^{2}

Solution

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{32}{9})

Solution steps

f^{'} (x) = 72 x^{2} - 48 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = 0

into

24 x^{3} - 24 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{2}{3}

into

24 x^{3} - 24 x^{2} : - \frac{32}{9}

Minimum (\frac{2}{3}, - \frac{32}{9})

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{32}{9})

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Frequently Asked Questions (FAQ)

What is the extreme 24x^3-24x^2 ?
The extreme 24x^3-24x^2 is Maximum(0,0),Minimum(2/3 ,-32/9)