What is the extreme f(x)=(x+3)^{4/3},-6<= x<= 6 ?

The extreme f(x)=(x+3)^{4/3},-6<= x<= 6 is Maximum(-6,3*3^{1/3}),Minimum(-3,0),Maximum(6,9*9^{1/3})

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extreme f(x)=(x+3)^{4/3},-6<= x<= 6

extreme points

f (x) = (x + 3)^{\frac{4}{3}}, - 6 \leq x \leq 6

Maximum (- 6, 3 \cdot 3^{\frac{1}{3}}), Minimum (- 3, 0), Maximum (6, 9 \cdot 9^{\frac{1}{3}})

Solution steps

Find the critical points:

x = - 6, x = - 3, x = 6

Domain of

(x + 3)^{\frac{4}{3}}, - 6 \leq x \leq 6 : - 6 \leq x \leq 6

Find intervals:

Decreasing

: - 6 < x < - 3,

Increasing

: - 3 < x < 6

Plug the extreme point

x = - 6

into

(x + 3)^{\frac{4}{3}} \Rightarrow y = 3 3^{\frac{1}{3}}

Maximum (- 6, 3 \cdot 3^{\frac{1}{3}})

Plug the extreme point

x = - 3

into

(x + 3)^{\frac{4}{3}} \Rightarrow y = 0

Minimum (- 3, 0)

Plug the extreme point

x = 6

into

(x + 3)^{\frac{4}{3}} \Rightarrow y = 9 9^{\frac{1}{3}}

Maximum (6, 9 \cdot 9^{\frac{1}{3}})

Maximum (- 6, 3 \cdot 3^{\frac{1}{3}}), Minimum (- 3, 0), Maximum (6, 9 \cdot 9^{\frac{1}{3}})

x y - 2 x - 2 y - x^{2} - y^{2}

f (x) = 25 x - 25 x e^{- y} - 50 y - x^{2}

f (x) = csc^{2} (x) - \frac{2}{3} cot (x)

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

f (x) = 3 - x

What is the extreme f(x)=(x+3)^{4/3},-6<= x<= 6 ?
The extreme f(x)=(x+3)^{4/3},-6<= x<= 6 is Maximum(-6,3*3^{1/3}),Minimum(-3,0),Maximum(6,9*9^{1/3})