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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{5}{3}

into

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

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

Plug

x = \frac{5}{3}

into

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

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

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

Popular Examples

domain of f(x)= 3/x+6 domain

f (x) = \frac{3}{x} + 6

domain of x^2-4x+5 domain

x^{2} - 4 x + 5

intercepts of f(x)=3x^2+6x-4 intercepts

f (x) = 3 x^{2} + 6 x - 4

domain of f(x)=sqrt(3-3e^x)domain

f (x) = 3 - 3 e^{x}

inflection x^3-3x^2 inflection points

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

Frequently Asked Questions (FAQ)

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