What is the extreme f(x)=-1/2 x^4+16x^2-15 ?

The extreme f(x)=-1/2 x^4+16x^2-15 is Maximum(-4,113),Minimum(0,-15),Maximum(4,113)

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extreme f(x)=-1/2 x^4+16x^2-15

extreme points

f (x) = - \frac{1}{2} x^{4} + 16 x^{2} - 15

Maximum (- 4, 113), Minimum (0, - 15), Maximum (4, 113)

Solution steps

f^{'} (x) = - 2 x^{3} + 32 x

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

- \frac{1}{2} x^{4} + 16 x^{2} - 15 : 113

Maximum (- 4, 113)

Plug

x = 0

into

- \frac{1}{2} x^{4} + 16 x^{2} - 15 : - 15

Minimum (0, - 15)

Plug

x = 4

into

- \frac{1}{2} x^{4} + 16 x^{2} - 15 : 113

Maximum (4, 113)

Maximum (- 4, 113), Minimum (0, - 15), Maximum (4, 113)

f (x) = 10 x^{\frac{3}{4}} e^{- x}

f (x) = 2 x - 4 y + 6 z = 56

y = 1 - x^{2} - z^{2}

20 x^{2} - 200 x + 3

y = \frac{x ^{4}}{1 + x ^{3}}

What is the extreme f(x)=-1/2 x^4+16x^2-15 ?
The extreme f(x)=-1/2 x^4+16x^2-15 is Maximum(-4,113),Minimum(0,-15),Maximum(4,113)