What is the extreme (x^4-4x^3),-1<= x<= 4 ?

The extreme (x^4-4x^3),-1<= x<= 4 is Maximum(-1,5),Saddle(0,0),Minimum(3,-27),Maximum(4,0)

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extreme (x^4-4x^3),-1<= x<= 4

extreme points

(x^{4} - 4 x^{3}), - 1 \leq x \leq 4

Maximum (- 1, 5), Saddle (0, 0), Minimum (3, - 27), Maximum (4, 0)

Solution steps

Find the critical points:

x = - 1, x = 0, x = 3, x = 4

Domain of

x^{4} - 4 x^{3}, - 1 \leq x \leq 4 : - 1 \leq x \leq 4

Find intervals:

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < 4

Plug the extreme point

x = - 1

into

x^{4} - 4 x^{3} \Rightarrow y = 5

Maximum (- 1, 5)

Plug the extreme point

x = 0

into

x^{4} - 4 x^{3} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = 3

into

x^{4} - 4 x^{3} \Rightarrow y = - 27

Minimum (3, - 27)

Plug the extreme point

x = 4

into

x^{4} - 4 x^{3} \Rightarrow y = 0

Maximum (4, 0)

Maximum (- 1, 5), Saddle (0, 0), Minimum (3, - 27), Maximum (4, 0)

f (x) = x - 2 cos (x)

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

f (x) = x^{\frac{1}{3}} + 2 x^{\frac{4}{3}}

f (x) = x^{3} - 2 x^{2} + 4

f (x) = \frac{4 x}{x ^{2} + 9}, - 4 \leq x \leq 4

What is the extreme (x^4-4x^3),-1<= x<= 4 ?
The extreme (x^4-4x^3),-1<= x<= 4 is Maximum(-1,5),Saddle(0,0),Minimum(3,-27),Maximum(4,0)