What is the extreme 5x^2+3,-1<= x<= 2 ?

The extreme 5x^2+3,-1<= x<= 2 is Maximum(-1,8),Minimum(0,3),Maximum(2,23)

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extreme 5x^2+3,-1<= x<= 2

extreme points

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

Maximum (- 1, 8), Minimum (0, 3), Maximum (2, 23)

Solution steps

Find the critical points:

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

Domain of

5 x^{2} + 3, - 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} + 3 \Rightarrow y = 8

Maximum (- 1, 8)

Plug the extreme point

x = 0

into

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

Minimum (0, 3)

Plug the extreme point

x = 2

into

5 x^{2} + 3 \Rightarrow y = 23

Maximum (2, 23)

Maximum (- 1, 8), Minimum (0, 3), Maximum (2, 23)

f (x) = x^{4} - 6 x^{\frac{3}{2}}, x > 0

f (0.1, 0) = (2 x - x^{2}) (2 y - y^{2})

f (x) = 600 t - 15 t^{2}

f (x, y) = x + y + 5

f (x) = 2 x^{4} - x^{2} + 1

What is the extreme 5x^2+3,-1<= x<= 2 ?
The extreme 5x^2+3,-1<= x<= 2 is Maximum(-1,8),Minimum(0,3),Maximum(2,23)