What is the extreme f(x)=5-3x^2,-5<= x<= 1 ?

The extreme f(x)=5-3x^2,-5<= x<= 1 is Minimum(-5,-70),Maximum(0,5),Minimum(1,2)

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extreme f(x)=5-3x^2,-5<= x<= 1

extreme points

f (x) = 5 - 3 x^{2}, - 5 \leq x \leq 1

Minimum (- 5, - 70), Maximum (0, 5), Minimum (1, 2)

Solution steps

Find the critical points:

x = - 5, x = 0, x = 1

Domain of

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

Find intervals:

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 1

Plug the extreme point

x = - 5

into

5 - 3 x^{2} \Rightarrow y = - 70

Minimum (- 5, - 70)

Plug the extreme point

x = 0

into

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

Maximum (0, 5)

Plug the extreme point

x = 1

into

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

Minimum (1, 2)

Minimum (- 5, - 70), Maximum (0, 5), Minimum (1, 2)

f (x) = 16 x + 21 x^{\frac{16}{21}}

e^{- y} (x^{2} + y^{2})

f (x) = x^{\frac{2}{3}} (x - 3), - 3 \leq x \leq 3

f (x) = 2 x^{3} - 27 x^{2} + 84 x + 11

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

What is the extreme f(x)=5-3x^2,-5<= x<= 1 ?
The extreme f(x)=5-3x^2,-5<= x<= 1 is Minimum(-5,-70),Maximum(0,5),Minimum(1,2)