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Popular Functions >

extreme f(x)=(8x)^3-(5x)^2-3x

Solution

extreme points

f (x) = (8 x)^{3} - (5 x)^{2} - 3 x

Solution

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Solution steps

f^{'} (x) = 1536 x^{2} - 50 x - 3

Find intervals:

Increasing

: - \infty < x < \frac{- 5233 + 25}{1536},

Decreasing

: \frac{- 5233 + 25}{1536} < x < \frac{5233 + 25}{1536},

Increasing

: \frac{5233 + 25}{1536} < x < \infty

Plug

x = \frac{25 - 5233}{1536}

into

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{5233 5233 - 188425}{3538944}

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944})

Plug

x = \frac{25 + 5233}{1536}

into

(8 x)^{3} - (5 x)^{2} - 3 x : \frac{- 188425 - 5233 5233}{3538944}

Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Maximum (\frac{25 - 5233}{1536}, \frac{5233 5233 - 188425}{3538944}), Minimum (\frac{25 + 5233}{1536}, \frac{- 188425 - 5233 5233}{3538944})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(8x)^3-(5x)^2-3x ?
The extreme f(x)=(8x)^3-(5x)^2-3x is