What is the extreme f(x)=x^5-10x^4-1=x^4(x-10)-1 ?

The extreme f(x)=x^5-10x^4-1=x^4(x-10)-1 is Maximum(0,-1),Minimum(8,-8193)

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extreme f(x)=x^5-10x^4-1=x^4(x-10)-1

extreme points

f (x) = x^{5} - 10 x^{4} - 1 = x^{4} (x - 10) - 1

Maximum (0, - 1), Minimum (8, - 8193)

Solution steps

f^{'} (x) = 5 x^{3} (x - 8)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

x^{4} (x - 10) - 1 : - 1

Maximum (0, - 1)

Plug

x = 8

into

x^{4} (x - 10) - 1 : - 8193

Minimum (8, - 8193)

Maximum (0, - 1), Minimum (8, - 8193)

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 4, - 2 \leq x \leq 5

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

f (x) = x^{2} - 12 x + 5

f (x) = x^{2} - y^{2} + 21

f (x, y) = (9 x^{2} + 4 x + 5) (9 y^{2} + 6 y + 6)

What is the extreme f(x)=x^5-10x^4-1=x^4(x-10)-1 ?
The extreme f(x)=x^5-10x^4-1=x^4(x-10)-1 is Maximum(0,-1),Minimum(8,-8193)