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Popular >

extreme (x+3)(x-6)^2

Solution

extreme points

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

Solution

Maximum (0, 108), Minimum (6, 0)

Solution steps

f^{'} (x) = 3 x (x - 6)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

(x + 3) (x - 6)^{2} : 108

Maximum (0, 108)

Plug

x = 6

into

(x + 3) (x - 6)^{2} : 0

Minimum (6, 0)

Maximum (0, 108), Minimum (6, 0)

Popular Examples

extreme f(x)=x^4-18x^2+1,-6<= x<= 6 extreme points

f (x) = x^{4} - 18 x^{2} + 1, - 6 \leq x \leq 6

extreme f(x)=3x^5-25x^3+60x extreme points

f (x) = 3 x^{5} - 25 x^{3} + 60 x

extreme x^2+xy+y^2-7x-3y extreme points

x^{2} + x y + y^{2} - 7 x - 3 y

extreme 10x^{1/2}-x[100]extreme points

10 x^{\frac{1}{2}} - x [100]

extreme f(x)=2x^3-2x^2-2x+6 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme (x+3)(x-6)^2 ?
The extreme (x+3)(x-6)^2 is Maximum(0,108),Minimum(6,0)