What is the extreme f(x)=x^2-6,-2<= x<= 4 ?

The extreme f(x)=x^2-6,-2<= x<= 4 is Maximum(-2,-2),Minimum(0,-6),Maximum(4,10)

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extreme f(x)=x^2-6,-2<= x<= 4

extreme points

f (x) = x^{2} - 6, - 2 \leq x \leq 4

Maximum (- 2, - 2), Minimum (0, - 6), Maximum (4, 10)

Solution steps

Find the critical points:

x = - 2, x = 0, x = 4

Domain of

x^{2} - 6, - 2 \leq x \leq 4 : - 2 \leq x \leq 4

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 4

Plug the extreme point

x = - 2

into

x^{2} - 6 \Rightarrow y = - 2

Maximum (- 2, - 2)

Plug the extreme point

x = 0

into

x^{2} - 6 \Rightarrow y = - 6

Minimum (0, - 6)

Plug the extreme point

x = 4

into

x^{2} - 6 \Rightarrow y = 10

Maximum (4, 10)

Maximum (- 2, - 2), Minimum (0, - 6), Maximum (4, 10)

f (x, y) = e^{- 2 x^{2} - 4 y^{2}}

6 x^{2} - 48 x - 190

f (x) = \frac{e ^{x}}{( 4 + e ^{x} )}

f (x) = 4 x^{3} - 2 x^{2} - 5

T (x, y) = ln (3 x y + 2 x^{2} - y)

What is the extreme f(x)=x^2-6,-2<= x<= 4 ?
The extreme f(x)=x^2-6,-2<= x<= 4 is Maximum(-2,-2),Minimum(0,-6),Maximum(4,10)