What is the extreme f(x)=x^5-20x^4+8,0<= x<= 17 ?

The extreme f(x)=x^5-20x^4+8,0<= x<= 17 is Maximum(0,8),Minimum(16,-262136),Maximum(17,-250555)

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extreme f(x)=x^5-20x^4+8,0<= x<= 17

extreme points

f (x) = x^{5} - 20 x^{4} + 8, 0 \leq x \leq 17

Maximum (0, 8), Minimum (16, - 262136), Maximum (17, - 250555)

Solution steps

Find the critical points:

x = 0, x = 16, x = 17

Domain of

x^{5} - 20 x^{4} + 8, 0 \leq x \leq 17 : 0 \leq x \leq 17

Find intervals:

Decreasing

: 0 < x < 16,

Increasing

: 16 < x < 17

Plug the extreme point

x = 0

into

x^{5} - 20 x^{4} + 8 \Rightarrow y = 8

Maximum (0, 8)

Plug the extreme point

x = 16

into

x^{5} - 20 x^{4} + 8 \Rightarrow y = - 262136

Minimum (16, - 262136)

Plug the extreme point

x = 17

into

x^{5} - 20 x^{4} + 8 \Rightarrow y = - 250555

Maximum (17, - 250555)

Maximum (0, 8), Minimum (16, - 262136), Maximum (17, - 250555)

P (q, r) = 4 - q + r

\frac{d}{d x} (I n 1 - 2 x)

y = x^{2} - 12 x + 35

3 x^{2} - 3

f (x) = - \frac{5}{x ^{2}}

What is the extreme f(x)=x^5-20x^4+8,0<= x<= 17 ?
The extreme f(x)=x^5-20x^4+8,0<= x<= 17 is Maximum(0,8),Minimum(16,-262136),Maximum(17,-250555)