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Popular >

extreme y=-x^3+6x^2

Solution

extreme points

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

Solution

Minimum (0, 0), Maximum (4, 32)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 4

into

- x^{3} + 6 x^{2} : 32

Maximum (4, 32)

Minimum (0, 0), Maximum (4, 32)

Graph

Popular Examples

extreme f(x,y)=-3x^2+2xy-y^2+14x+2y+10 extreme points

f (x, y) = - 3 x^{2} + 2 x y - y^{2} + 14 x + 2 y + 10

extreme f(x)=x^2log_{6}(x)extreme points

f (x) = x^{2} lo g_{6} (x)

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y = \frac{ln ( x )}{x ^{4}}

extreme 250+8x^3+x^4 extreme points

250 + 8 x^{3} + x^{4}

extreme f(x)=e^{3x^2+8y^2+13}extreme points

f (x) = e^{3 x^{2} + 8 y^{2} + 13}

Frequently Asked Questions (FAQ)

What is the extreme y=-x^3+6x^2 ?
The extreme y=-x^3+6x^2 is Minimum(0,0),Maximum(4,32)