What is the extreme f(x)=x^4-24x^2+64x+16 ?

The extreme f(x)=x^4-24x^2+64x+16 is Minimum(-4,-368),Saddle(2,64)

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extreme f(x)=x^4-24x^2+64x+16

extreme points

f (x) = x^{4} - 24 x^{2} + 64 x + 16

Minimum (- 4, - 368), Saddle (2, 64)

Solution steps

f^{'} (x) = 4 x^{3} - 48 x + 64

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

x^{4} - 24 x^{2} + 64 x + 16 : - 368

Minimum (- 4, - 368)

Plug

x = 2

into

x^{4} - 24 x^{2} + 64 x + 16 : 64

Saddle (2, 64)

Minimum (- 4, - 368), Saddle (2, 64)

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

f (x) = \frac{x ^{3}}{e ^{8 x}}

f (x) = x e^{- \frac{x ^{2}}{32}}

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}}

f (x) = \frac{x}{x - 2}, 3 \leq x \leq 4

What is the extreme f(x)=x^4-24x^2+64x+16 ?
The extreme f(x)=x^4-24x^2+64x+16 is Minimum(-4,-368),Saddle(2,64)