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Popular >

extreme x^3-9x^2+1

Solution

extreme points

x^{3} - 9 x^{2} + 1

Solution

Maximum (0, 1), Minimum (6, - 107)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

x^{3} - 9 x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 6

into

x^{3} - 9 x^{2} + 1 : - 107

Minimum (6, - 107)

Maximum (0, 1), Minimum (6, - 107)

Popular Examples

extreme f(x)=(-24x^2-20x+24)/((x^2+1)^2)extreme points

f (x) = \frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}}

extreme f(x)=x^2+y^2+20x-8y extreme points

f (x) = x^{2} + y^{2} + 20 x - 8 y

extreme f(x)=x+y+8/(xy)extreme points

f (x) = x + y + \frac{8}{x y}

extreme f(x)=-15051x^2+47796x+13402 extreme points

f (x) = - 15051 x^{2} + 47796 x + 13402

extreme y=-3x^5+5x^3+1 extreme points

y = - 3 x^{5} + 5 x^{3} + 1

Frequently Asked Questions (FAQ)

What is the extreme x^3-9x^2+1 ?
The extreme x^3-9x^2+1 is Maximum(0,1),Minimum(6,-107)