What is the extreme f(x)=x^3+2,-1<= x<= 2 ?

The extreme f(x)=x^3+2,-1<= x<= 2 is Minimum(-1,1),Saddle(0,2),Maximum(2,10)

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extreme f(x)=x^3+2,-1<= x<= 2

extreme points

f (x) = x^{3} + 2, - 1 \leq x \leq 2

Minimum (- 1, 1), Saddle (0, 2), Maximum (2, 10)

Solution steps

Find the critical points:

x = - 1, x = 0, x = 2

Domain of

x^{3} + 2, - 1 \leq x \leq 2 : - 1 \leq x \leq 2

Find intervals:

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < 2

Plug the extreme point

x = - 1

into

x^{3} + 2 \Rightarrow y = 1

Minimum (- 1, 1)

Plug the extreme point

x = 0

into

x^{3} + 2 \Rightarrow y = 2

Saddle (0, 2)

Plug the extreme point

x = 2

into

x^{3} + 2 \Rightarrow y = 10

Maximum (2, 10)

Minimum (- 1, 1), Saddle (0, 2), Maximum (2, 10)

f (x) = x x - 5

f (x) = 2 x^{4} - 24 x^{3} + 20

\frac{760}{x} + 2 π x^{2}

+ x - 1

f (x) = 3 x^{3} + 8, - 2 \leq x \leq 2

What is the extreme f(x)=x^3+2,-1<= x<= 2 ?
The extreme f(x)=x^3+2,-1<= x<= 2 is Minimum(-1,1),Saddle(0,2),Maximum(2,10)