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

The extreme f(x)=-x^3+5x^2+8x+3 is Minimum(-2/3 , 5/27),Maximum(4,51)

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

extreme points

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

Minimum (- \frac{2}{3}, \frac{5}{27}), Maximum (4, 51)

Solution steps

f^{'} (x) = - 3 x^{2} + 10 x + 8

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} + 5 x^{2} + 8 x + 3 : \frac{5}{27}

Minimum (- \frac{2}{3}, \frac{5}{27})

Plug

x = 4

into

- x^{3} + 5 x^{2} + 8 x + 3 : 51

Maximum (4, 51)

Minimum (- \frac{2}{3}, \frac{5}{27}), Maximum (4, 51)

What is the extreme f(x)=-x^3+5x^2+8x+3 ?
The extreme f(x)=-x^3+5x^2+8x+3 is Minimum(-2/3 , 5/27),Maximum(4,51)