What is the extreme f(x)=(x^3-64)^4 ?

The extreme f(x)=(x^3-64)^4 is Saddle(0,16777216),Minimum(4,0)

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extreme f(x)=(x^3-64)^4

extreme points

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

Saddle (0, 16777216), Minimum (4, 0)

Solution steps

f^{'} (x) = 12 x^{2} (x^{3} - 64)^{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

(x^{3} - 64)^{4} : 16777216

Saddle (0, 16777216)

Plug

x = 4

into

(x^{3} - 64)^{4} : 0

Minimum (4, 0)

Saddle (0, 16777216), Minimum (4, 0)

f (x, y) = 7 x^{2} + 7 x y + 10 y^{2} + 7 x y^{2} + 4 x^{2} y

\frac{3}{x} - 1

\frac{2 x}{9 - x ^{2}}

y (θ) = tan^{2} (θ) - 1, - \frac{π}{2} < θ < \frac{π}{2}

f (x) = 17 + 2 x - x^{2}, 0 \leq x \leq 5

What is the extreme f(x)=(x^3-64)^4 ?
The extreme f(x)=(x^3-64)^4 is Saddle(0,16777216),Minimum(4,0)