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Popular >

extreme f(x)=-x^3+5x+9

Solution

extreme points

f (x) = - x^{3} + 5 x + 9

Solution

Minimum (- \frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 9), Maximum (\frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 9)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{3},

Increasing

: - \frac{5}{3} < x < \frac{5}{3},

Decreasing

: \frac{5}{3} < x < \infty

Plug

x = - \frac{5}{3}

into

- x^{3} + 5 x + 9 : (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 9

Minimum (- \frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 9)

Plug

x = \frac{5}{3}

into

- x^{3} + 5 x + 9 : - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 9

Maximum (\frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 9)

Minimum (- \frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 9), Maximum (\frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 9)

Popular Examples

domain of f(x)=(sqrt(5+x))/(9-x)domain

f (x) = \frac{5 + x}{9 - x}

intercepts of f(x)=((-x^4)/4)+x^2-1 intercepts

f (x) = (\frac{- x ^{4}}{4}) + x^{2} - 1

distance (4,5),(3,2)distance

(4, 5), (3, 2)

intercepts of f(x)=(5x)/(x-2)intercepts

f (x) = \frac{5 x}{x - 2}

extreme f(x)=(x+3)/(3-x)extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=-x^3+5x+9 ?
The extreme f(x)=-x^3+5x+9 is