Tuesday

March 31, 2015

March 31, 2015

Posted by **Elaine** on Tuesday, April 24, 2012 at 8:03pm.

a) find the x-intercepts algebraically

b) find all the critical points

c) use the first derivative test to determine local minimums and maximums

d)find all inflection points

e)state the concavity of the graph on appropriate intervals

- Calculus -
**Steve**, Wednesday, April 25, 2012 at 10:53ama) x=0, x=2

b)

f(x) = x^3(x-2)^2

f '(x) = 3x^2(x-2)^2 + 2x^3(x-2)

= x^2(x-2)(5x-6)

critical points at x=0,2,6/5

max/min are at (0,0)(2,0)(1.2,1.106)

inflection where f ''(x) = 0

f ''(x) = 4x(5x^2 - 12x + 6)

f ''(x) = 0 at x = .71, 1.69

plug in to obtain f(x) there

concave down: -oo < x < 0

concave up: 0 < x < .71

concave down: .71 < x < 1.69

concave up: 1.69 < x < oo

**Answer this Question**

**Related Questions**

Calculus - Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x ...

Calculus - Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x ...

calculus - Please help!! Okay so my teacher has been away and hasent explained ...

Calculus - Suppose that f(x)=3x^3+3x. Find all critical values of f. Then use ...

CURVE SKETCHING PLEASE HELP - Okay so my teacher has been away and hasent ...

Calculus-Function - sketch the graph of a function in neighborhood x=2 that ...

Math-Calculus (check please) - FOr the function f(x)=x^2e^x Find the critical ...

calculus - Use a graph of f(x) = 3 e^{-8 x^2} to estimate the x-values of any ...

calculus - Find the asymptote, interval of monotonicity, critical points, the ...

calculus - Find the asymptote, interval of monotonicity, critical points, the ...