What is the extreme f(x)=2x^3+3x^2-36x+1[-6.3] ?

The extreme f(x)=2x^3+3x^2-36x+1[-6.3] is Maximum(-3,74.7),Minimum(2,-50.3)

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extreme f(x)=2x^3+3x^2-36x+1[-6.3]

extreme points

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3]

Maximum (- 3, 74.7), Minimum (2, - 50.3)

Solution steps

f^{'} (x) = 6 x^{2} + 6 x - 36

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3] : 74.7

Maximum (- 3, 74.7)

Plug

x = 2

into

2 x^{3} + 3 x^{2} - 36 x + 1 [- 6.3] : - 50.3

Minimum (2, - 50.3)

Maximum (- 3, 74.7), Minimum (2, - 50.3)

f (x) = e^{3 x} (3 - x)

f (x) = 4 x^{3} + 6 x^{2} - 24 x

f (x) = x^{2} - x - 3, 0 \leq x \leq 3

f (x) = - 4 x^{6} ln (3 x)

f (x) = - x^{2} + 100 x + 8

What is the extreme f(x)=2x^3+3x^2-36x+1[-6.3] ?
The extreme f(x)=2x^3+3x^2-36x+1[-6.3] is Maximum(-3,74.7),Minimum(2,-50.3)