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

The extreme f(x)=5x^3+2x^2-3x is Maximum(-3/5 , 36/25),Minimum(1/3 ,-16/27)

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

extreme points

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

Maximum (- \frac{3}{5}, \frac{36}{25}), Minimum (\frac{1}{3}, - \frac{16}{27})

Solution steps

f^{'} (x) = 15 x^{2} + 4 x - 3

Find intervals:

Increasing

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

Decreasing

: - \frac{3}{5} < x < \frac{1}{3},

Increasing

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

Plug

x = - \frac{3}{5}

into

5 x^{3} + 2 x^{2} - 3 x : \frac{36}{25}

Maximum (- \frac{3}{5}, \frac{36}{25})

Plug

x = \frac{1}{3}

into

5 x^{3} + 2 x^{2} - 3 x : - \frac{16}{27}

Minimum (\frac{1}{3}, - \frac{16}{27})

Maximum (- \frac{3}{5}, \frac{36}{25}), Minimum (\frac{1}{3}, - \frac{16}{27})

What is the extreme f(x)=5x^3+2x^2-3x ?
The extreme f(x)=5x^3+2x^2-3x is Maximum(-3/5 , 36/25),Minimum(1/3 ,-16/27)