What is the extreme f(x)=5x^2+1,-1<= x<= 2 ?

The extreme f(x)=5x^2+1,-1<= x<= 2 is Maximum(-1,6),Minimum(0,1),Maximum(2,21)

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extreme f(x)=5x^2+1,-1<= x<= 2

extreme

Maximum (- 1, 6), Minimum (0, 1), Maximum (2, 21)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 2

Plug the extreme point

x = - 1

into

5 x^{2} + 1 \Rightarrow y = 6

Maximum (- 1, 6)

Plug the extreme point

x = 0

into

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

Minimum (0, 1)

Plug the extreme point

x = 2

into

5 x^{2} + 1 \Rightarrow y = 21

Maximum (2, 21)

Maximum (- 1, 6), Minimum (0, 1), Maximum (2, 21)

What is the extreme f(x)=5x^2+1,-1<= x<= 2 ?
The extreme f(x)=5x^2+1,-1<= x<= 2 is Maximum(-1,6),Minimum(0,1),Maximum(2,21)