What is the extreme f(x)=-1/2 x^4+2x^3+28x^2+18 ?

The extreme f(x)=-1/2 x^4+2x^3+28x^2+18 is Maximum(-4,210),Minimum(0,18),Maximum(7, 1751/2)

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extreme f(x)=-1/2 x^4+2x^3+28x^2+18

extreme points

f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18

Maximum (- 4, 210), Minimum (0, 18), Maximum (7, \frac{1751}{2})

Solution steps

f^{'} (x) = - 2 x^{3} + 6 x^{2} + 56 x

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 4

into

- \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18 : 210

Maximum (- 4, 210)

Plug

x = 0

into

- \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18 : 18

Minimum (0, 18)

Plug

x = 7

into

- \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18 : \frac{1751}{2}

Maximum (7, \frac{1751}{2})

Maximum (- 4, 210), Minimum (0, 18), Maximum (7, \frac{1751}{2})

f (x, y) = ln (x + y - 4)

f (x, y) = x^{2} + x y + y^{2} - 37 y + 456

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

3 x^{5} - 5 x^{3} + 1

f (x) = 2 sin (x) - cos (2 x), 0 \leq x \leq 2 π

What is the extreme f(x)=-1/2 x^4+2x^3+28x^2+18 ?
The extreme f(x)=-1/2 x^4+2x^3+28x^2+18 is Maximum(-4,210),Minimum(0,18),Maximum(7, 1751/2)