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Popular >

extreme f(x)=4-x^3+5x

Solution

extreme points

f (x) = 4 - x^{3} + 5 x

Solution

Minimum (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}), Maximum (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{3},

Increasing

: - \frac{5}{3} < x < \frac{5}{3},

Decreasing

: \frac{5}{3} < x < \infty

Plug

x = - \frac{5}{3}

into

4 - x^{3} + 5 x : 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}

Minimum (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3})

Plug

x = \frac{5}{3}

into

4 - x^{3} + 5 x : 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3}

Maximum (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

Minimum (- \frac{5}{3}, 4 + (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3}), Maximum (\frac{5}{3}, 4 - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=4-x^3+5x ?
The extreme f(x)=4-x^3+5x is