What is the extreme 2x^3+6x^2-90x+7,-5<= x<= 6 ?

The extreme 2x^3+6x^2-90x+7,-5<= x<= 6 is Maximum(-5,357),Minimum(3,-155),Maximum(6,115)

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extreme 2x^3+6x^2-90x+7,-5<= x<= 6

extreme points

2 x^{3} + 6 x^{2} - 90 x + 7, - 5 \leq x \leq 6

Maximum (- 5, 357), Minimum (3, - 155), Maximum (6, 115)

Solution steps

Find the critical points:

x = - 5, x = 3, x = 6

Domain of

2 x^{3} + 6 x^{2} - 90 x + 7, - 5 \leq x \leq 6 : - 5 \leq x \leq 6

Find intervals:

Decreasing

: - 5 < x < 3,

Increasing

: 3 < x < 6

Plug the extreme point

x = - 5

into

2 x^{3} + 6 x^{2} - 90 x + 7 \Rightarrow y = 357

Maximum (- 5, 357)

Plug the extreme point

x = 3

into

2 x^{3} + 6 x^{2} - 90 x + 7 \Rightarrow y = - 155

Minimum (3, - 155)

Plug the extreme point

x = 6

into

2 x^{3} + 6 x^{2} - 90 x + 7 \Rightarrow y = 115

Maximum (6, 115)

Maximum (- 5, 357), Minimum (3, - 155), Maximum (6, 115)

f (x) = - \frac{5}{4} x^{2} + \frac{5}{2} x + \frac{7}{4}

f (x, y) = x + y - \frac{3}{2} (x^{2} + y^{2} + 1)

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

- x^{2} + 8 x - 9

f (x) = x^{3} - 12 x^{2} - 27 x + 2, 1 \leq x \leq 10

What is the extreme 2x^3+6x^2-90x+7,-5<= x<= 6 ?
The extreme 2x^3+6x^2-90x+7,-5<= x<= 6 is Maximum(-5,357),Minimum(3,-155),Maximum(6,115)