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

The extreme-x^2+3x+5,-3<= x<= 3 is Minimum(-3,-13),Maximum(3/2 , 29/4),Minimum(3,5)

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

extreme points

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

Minimum (- 3, - 13), Maximum (\frac{3}{2}, \frac{29}{4}), Minimum (3, 5)

Solution steps

Find the critical points:

x = - 3, x = \frac{3}{2}, x = 3

Domain of

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

Find intervals:

Increasing

: - 3 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < 3

Plug the extreme point

x = - 3

into

- x^{2} + 3 x + 5 \Rightarrow y = - 13

Minimum (- 3, - 13)

Plug the extreme point

x = \frac{3}{2}

into

- x^{2} + 3 x + 5 \Rightarrow y = \frac{29}{4}

Maximum (\frac{3}{2}, \frac{29}{4})

Plug the extreme point

x = 3

into

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

Minimum (3, 5)

Minimum (- 3, - 13), Maximum (\frac{3}{2}, \frac{29}{4}), Minimum (3, 5)

72 x + 3 x^{2} - 2 x^{3}

f (x) = 2 x^{3} - x^{2} - 4 x + 12

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

f (x) = x^{3} - 3 x^{2} + 7 x - 10

f (x) = - 10 x^{2} - 40 x - 2

What is the extreme-x^2+3x+5,-3<= x<= 3 ?
The extreme-x^2+3x+5,-3<= x<= 3 is Minimum(-3,-13),Maximum(3/2 , 29/4),Minimum(3,5)