What is the extreme h(x)=5(x-1)^{2/3},0<= x<= 2 ?

The extreme h(x)=5(x-1)^{2/3},0<= x<= 2 is Maximum(0,5),Minimum(1,0),Maximum(2,5)

extreme h(x)=5(x-1)^{2/3},0<= x<= 2

extreme points

h (x) = 5 (x - 1)^{\frac{2}{3}}, 0 \leq x \leq 2

Maximum (0, 5), Minimum (1, 0), Maximum (2, 5)

Solution steps

Find the critical points:

x = 0, x = 1, x = 2

Domain of

5 (x - 1)^{\frac{2}{3}}, 0 \leq x \leq 2 : 0 \leq x \leq 2

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 2

Plug the extreme point

x = 0

into

5 (x - 1)^{\frac{2}{3}} \Rightarrow y = 5

Maximum (0, 5)

Plug the extreme point

x = 1

into

5 (x - 1)^{\frac{2}{3}} \Rightarrow y = 0

Minimum (1, 0)

Plug the extreme point

x = 2

into

5 (x - 1)^{\frac{2}{3}} \Rightarrow y = 5

Maximum (2, 5)

Maximum (0, 5), Minimum (1, 0), Maximum (2, 5)

f (x) = - 4 x^{3} + 6 x^{2} + 6

f (x, y) = \frac{5}{2} x^{2} + x y^{2} + 5 y^{2}

f (x) = (3 6 x^{2} - x^{3})

f (x) = 7 x^{3} - 7 x^{2} + 7

y = - \frac{4 x}{x ^{2} + 1}

What is the extreme h(x)=5(x-1)^{2/3},0<= x<= 2 ?
The extreme h(x)=5(x-1)^{2/3},0<= x<= 2 is Maximum(0,5),Minimum(1,0),Maximum(2,5)