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Popular >

extreme x^3-x^2-x+7

Solution

extreme points

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

Solution

Maximum (- \frac{1}{3}, \frac{194}{27}), Minimum (1, 6)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - x^{2} - x + 7 : \frac{194}{27}

Maximum (- \frac{1}{3}, \frac{194}{27})

Plug

x = 1

into

x^{3} - x^{2} - x + 7 : 6

Minimum (1, 6)

Maximum (- \frac{1}{3}, \frac{194}{27}), Minimum (1, 6)

Popular Examples

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f (x) = x^{5} y^{2} - 3 x^{3} + 10 + 5 y^{3} - x y

extreme f(x)=(0.2t)/(t^2+59)extreme points

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f (x) = 3 x^{2} - 4 x + 12

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f (x) = x (- \frac{2 x}{3} + 4)

Frequently Asked Questions (FAQ)

What is the extreme x^3-x^2-x+7 ?
The extreme x^3-x^2-x+7 is Maximum(-1/3 , 194/27),Minimum(1,6)