What is the extreme f(x)=2x^3+4x^2-1 ?

The extreme f(x)=2x^3+4x^2-1 is Maximum(-4/3 , 37/27),Minimum(0,-1)

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extreme f(x)=2x^3+4x^2-1

extreme

Maximum (- \frac{4}{3}, \frac{37}{27}), Minimum (0, - 1)

Solution steps

f^{'} (x) = 6 x^{2} + 8 x

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{4}{3}

into

2 x^{3} + 4 x^{2} - 1 : \frac{37}{27}

Maximum (- \frac{4}{3}, \frac{37}{27})

Plug

x = 0

into

2 x^{3} + 4 x^{2} - 1 : - 1

Minimum (0, - 1)

Maximum (- \frac{4}{3}, \frac{37}{27}), Minimum (0, - 1)

What is the extreme f(x)=2x^3+4x^2-1 ?
The extreme f(x)=2x^3+4x^2-1 is Maximum(-4/3 , 37/27),Minimum(0,-1)