What is the extreme f(x)=5-6x^2,-4<= x<= 2 ?

The extreme f(x)=5-6x^2,-4<= x<= 2 is Minimum(-4,-91),Maximum(0,5),Minimum(2,-19)

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extreme f(x)=5-6x^2,-4<= x<= 2

extreme points

f (x) = 5 - 6 x^{2}, - 4 \leq x \leq 2

Minimum (- 4, - 91), Maximum (0, 5), Minimum (2, - 19)

Solution steps

Find the critical points:

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

Domain of

5 - 6 x^{2}, - 4 \leq x \leq 2 : - 4 \leq x \leq 2

Find intervals:

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 2

Plug the extreme point

x = - 4

into

5 - 6 x^{2} \Rightarrow y = - 91

Minimum (- 4, - 91)

Plug the extreme point

x = 0

into

5 - 6 x^{2} \Rightarrow y = 5

Maximum (0, 5)

Plug the extreme point

x = 2

into

5 - 6 x^{2} \Rightarrow y = - 19

Minimum (2, - 19)

Minimum (- 4, - 91), Maximum (0, 5), Minimum (2, - 19)

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

e^{9 x} + e^{- x}

f (x) = x^{3} - 3 x y^{2} - 3 y^{2} + 12 y

x^{2} y - 6 y^{2} - 3 x^{2}

f (x) = - x^{2} + 7 x - 7

What is the extreme f(x)=5-6x^2,-4<= x<= 2 ?
The extreme f(x)=5-6x^2,-4<= x<= 2 is Minimum(-4,-91),Maximum(0,5),Minimum(2,-19)