What is the extreme xsqrt(36-x^2) ?

The extreme xsqrt(36-x^2) is Maximum(-6,0),Minimum(-3sqrt(2),-18),Maximum(3sqrt(2),18),Minimum(6,0)

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extreme xsqrt(36-x^2)

extreme points

x 36 - x^{2}

Maximum (- 6, 0), Minimum (- 32, - 18), Maximum (32, 18), Minimum (6, 0)

Solution steps

Find the critical points:

x = - 6, x = - 32, x = 32, x = 6

Domain of

x 36 - x^{2} : - 6 \leq x \leq 6

Find intervals:

Decreasing

: - 6 < x < - 32,

Increasing

: - 32 < x < 32,

Decreasing

: 32 < x < 6

Plug the extreme point

x = - 6

into

x 36 - x^{2} \Rightarrow y = 0

Maximum (- 6, 0)

Plug the extreme point

x = - 32

into

x 36 - x^{2} \Rightarrow y = - 18

Minimum (- 32, - 18)

Plug the extreme point

x = 32

into

x 36 - x^{2} \Rightarrow y = 18

Maximum (32, 18)

Plug the extreme point

x = 6

into

x 36 - x^{2} \Rightarrow y = 0

Minimum (6, 0)

Maximum (- 6, 0), Minimum (- 32, - 18), Maximum (32, 18), Minimum (6, 0)

x^{2} + \frac{640}{x}

f (x) = 2 x^{2} + \frac{10800}{x}

f (x, y) = x^{2} + y^{2} + 6 x - 4 y + 13

f (x) = (3 - 5 x) e^{2 x}

f (x) = 3 - 5 x^{2}

What is the extreme xsqrt(36-x^2) ?
The extreme xsqrt(36-x^2) is Maximum(-6,0),Minimum(-3sqrt(2),-18),Maximum(3sqrt(2),18),Minimum(6,0)