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Popular >

extreme 2x^3-9x

Solution

extreme points

2 x^{3} - 9 x

Solution

Maximum (- \frac{3}{2}, - 2 (\frac{3}{2})^{\frac{3}{2}} + 9 \frac{3}{2}), Minimum (\frac{3}{2}, 2 (\frac{3}{2})^{\frac{3}{2}} - 9 \frac{3}{2})

Solution steps

f^{'} (x) = 6 x^{2} - 9

Find intervals:

Increasing

: - \infty < x < - \frac{3}{2},

Decreasing

: - \frac{3}{2} < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

2 x^{3} - 9 x : - 2 (\frac{3}{2})^{\frac{3}{2}} + 9 \frac{3}{2}

Maximum (- \frac{3}{2}, - 2 (\frac{3}{2})^{\frac{3}{2}} + 9 \frac{3}{2})

Plug

x = \frac{3}{2}

into

2 x^{3} - 9 x : 2 (\frac{3}{2})^{\frac{3}{2}} - 9 \frac{3}{2}

Minimum (\frac{3}{2}, 2 (\frac{3}{2})^{\frac{3}{2}} - 9 \frac{3}{2})

Maximum (- \frac{3}{2}, - 2 (\frac{3}{2})^{\frac{3}{2}} + 9 \frac{3}{2}), Minimum (\frac{3}{2}, 2 (\frac{3}{2})^{\frac{3}{2}} - 9 \frac{3}{2})

Popular Examples

extreme f(x)=(2x^3-3x^2-12x+1)extreme points

f (x) = (2 x^{3} - 3 x^{2} - 12 x + 1)

extreme f(1)=x*e^y extreme points

f (1) = x \cdot e^{y}

extreme x^3+10x^2+x+1 extreme points

x^{3} + 10 x^{2} + x + 1

extreme f(x,y)=x^2+y^2+12x-14y extreme points

f (x, y) = x^{2} + y^{2} + 12 x - 14 y

extreme f(x)=-12x^5+135x^4-400x^3 extreme points

f (x) = - 12 x^{5} + 135 x^{4} - 400 x^{3}

Frequently Asked Questions (FAQ)

What is the extreme 2x^3-9x ?
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