What is the extreme 2x^3-33x^2+108x+5 ?

The extreme 2x^3-33x^2+108x+5 is Maximum(2,105),Minimum(9,-238)

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extreme 2x^3-33x^2+108x+5

extreme points

2 x^{3} - 33 x^{2} + 108 x + 5

Maximum (2, 105), Minimum (9, - 238)

Solution steps

f^{'} (x) = 6 x^{2} - 66 x + 108

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 2

into

2 x^{3} - 33 x^{2} + 108 x + 5 : 105

Maximum (2, 105)

Plug

x = 9

into

2 x^{3} - 33 x^{2} + 108 x + 5 : - 238

Minimum (9, - 238)

Maximum (2, 105), Minimum (9, - 238)

f (x) = x^{3} - \frac{3}{2} x^{2}, - 2 \leq x \leq 4

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

f (x) = x + \frac{4}{x}, 1 \leq x \leq 10

2 θ - 3 sin (θ)

f (x) = x^{2} + 2 x - 30

What is the extreme 2x^3-33x^2+108x+5 ?
The extreme 2x^3-33x^2+108x+5 is Maximum(2,105),Minimum(9,-238)