What is the extreme f(x)=-4x^3+3x^2+18x ?

The extreme f(x)=-4x^3+3x^2+18x is Minimum(-1,-11),Maximum(3/2 , 81/4)

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extreme f(x)=-4x^3+3x^2+18x

extreme points

f (x) = - 4 x^{3} + 3 x^{2} + 18 x

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

Solution steps

f^{'} (x) = - 12 x^{2} + 6 x + 18

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

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

Decreasing

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

Plug

x = - 1

into

- 4 x^{3} + 3 x^{2} + 18 x : - 11

Minimum (- 1, - 11)

Plug

x = \frac{3}{2}

into

- 4 x^{3} + 3 x^{2} + 18 x : \frac{81}{4}

Maximum (\frac{3}{2}, \frac{81}{4})

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

\frac{e ^{x}}{x}

f (x, y) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

f (x, y) = \frac{1}{25 - x ^{2} - y ^{2}}

f (x) = 1 - x^{2}

f (x, y) = 4 x^{2} y + 2 x y^{2} - 12 x y - 5

What is the extreme f(x)=-4x^3+3x^2+18x ?
The extreme f(x)=-4x^3+3x^2+18x is Minimum(-1,-11),Maximum(3/2 , 81/4)