What is the extreme f(x)=-x^3+3x^2+9x+10 ?

The extreme f(x)=-x^3+3x^2+9x+10 is Minimum(-1,5),Maximum(3,37)

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extreme f(x)=-x^3+3x^2+9x+10

extreme points

f (x) = - x^{3} + 3 x^{2} + 9 x + 10

Minimum (- 1, 5), Maximum (3, 37)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 9

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x^{2} + 9 x + 10 : 5

Minimum (- 1, 5)

Plug

x = 3

into

- x^{3} + 3 x^{2} + 9 x + 10 : 37

Maximum (3, 37)

Minimum (- 1, 5), Maximum (3, 37)

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

f (x, y) = 8 x^{3} - 12 x y + y^{3} + 11

f (x) = I x - 2 I + 1

f (x, y) = e^{- (x^{2} - y^{2})}

f (x, y) = x^{2} - 4 x y + 2 y^{2} + 4 x + 8 y + 7

What is the extreme f(x)=-x^3+3x^2+9x+10 ?
The extreme f(x)=-x^3+3x^2+9x+10 is Minimum(-1,5),Maximum(3,37)