What is the extreme f(x)=5x^4-x^5+4 ?

The extreme f(x)=5x^4-x^5+4 is Minimum(0,4),Maximum(4,260)

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extreme f(x)=5x^4-x^5+4

extreme points

f (x) = 5 x^{4} - x^{5} + 4

Minimum (0, 4), Maximum (4, 260)

Solution steps

f^{'} (x) = - 5 x^{4} + 20 x^{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

5 x^{4} - x^{5} + 4 : 4

Minimum (0, 4)

Plug

x = 4

into

5 x^{4} - x^{5} + 4 : 260

Maximum (4, 260)

Minimum (0, 4), Maximum (4, 260)

17 r^{2} - r^{3}

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

\frac{( 12 x ^{3} )}{3} + 38 x^{2} + 56 x, - 8 \leq x \leq 1

- x^{3} + 27 x - 58

y = x^{3} + 2 x

What is the extreme f(x)=5x^4-x^5+4 ?
The extreme f(x)=5x^4-x^5+4 is Minimum(0,4),Maximum(4,260)