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Popular >

extreme 4x^3-12x^2+8x

Solution

extreme points

4 x^{3} - 12 x^{2} + 8 x

Solution

Maximum (\frac{3 - 3}{3}, - 4 (4 - 23) + \frac{48 3 - 64}{3 3}), Minimum (\frac{3 + 3}{3}, - 4 (4 + 23) + \frac{48 3 + 64}{3 3})

Solution steps

f^{'} (x) = 12 x^{2} - 24 x + 8

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3} + 1,

Decreasing

: - \frac{1}{3} + 1 < x < \frac{1}{3} + 1,

Increasing

: \frac{1}{3} + 1 < x < \infty

Plug

x = \frac{3 - 3}{3}

into

4 x^{3} - 12 x^{2} + 8 x : - 4 (4 - 23) + \frac{48 3 - 64}{3 3}

Maximum (\frac{3 - 3}{3}, - 4 (4 - 23) + \frac{48 3 - 64}{3 3})

Plug

x = \frac{3 + 3}{3}

into

4 x^{3} - 12 x^{2} + 8 x : - 4 (4 + 23) + \frac{48 3 + 64}{3 3}

Minimum (\frac{3 + 3}{3}, - 4 (4 + 23) + \frac{48 3 + 64}{3 3})

Maximum (\frac{3 - 3}{3}, - 4 (4 - 23) + \frac{48 3 - 64}{3 3}), Minimum (\frac{3 + 3}{3}, - 4 (4 + 23) + \frac{48 3 + 64}{3 3})

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Frequently Asked Questions (FAQ)

What is the extreme 4x^3-12x^2+8x ?
The extreme 4x^3-12x^2+8x is