What is the extreme f(x)=-x^3+2x^2+15x-5 ?

The extreme f(x)=-x^3+2x^2+15x-5 is Minimum(-5/3 ,-535/27),Maximum(3,31)

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extreme f(x)=-x^3+2x^2+15x-5

extreme points

f (x) = - x^{3} + 2 x^{2} + 15 x - 5

Minimum (- \frac{5}{3}, - \frac{535}{27}), Maximum (3, 31)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 3 < x < \infty

Plug

x = - \frac{5}{3}

into

- x^{3} + 2 x^{2} + 15 x - 5 : - \frac{535}{27}

Minimum (- \frac{5}{3}, - \frac{535}{27})

Plug

x = 3

into

- x^{3} + 2 x^{2} + 15 x - 5 : 31

Maximum (3, 31)

Minimum (- \frac{5}{3}, - \frac{535}{27}), Maximum (3, 31)

f (x) = \frac{56 x + 49}{x ^{2}}

f (x) = \frac{5}{5 x - 16}

f (y) = 4 x + 12

\frac{x ^{3} - 3 x ^{2} - 4 x}{x - 4}

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

What is the extreme f(x)=-x^3+2x^2+15x-5 ?
The extreme f(x)=-x^3+2x^2+15x-5 is Minimum(-5/3 ,-535/27),Maximum(3,31)