Posted by Elaine on Tuesday, April 24, 2012 at 8:03pm.
assume that f(x)= x^3(x2)^2
a) find the xintercepts 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 10:53am
a) x=0, x=2
b)
f(x) = x^3(x2)^2
f '(x) = 3x^2(x2)^2 + 2x^3(x2)
= x^2(x2)(5x6)
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 ...
 Differential Calculus  Determine all local extrema, concavity and inflection ...
 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 ...
 CalculusFunction  sketch the graph of a function in neighborhood x=2 that ...
 calculus  Find the asymptote, interval of monotonicity, critical points, the ...
 calculus  Find the asymptote, interval of monotonicity, critical points, the ...
 calculus  Find the asymptote, interval of monotonicity, critical points, the ...
 calculus  Use a graph of f(x) = 3 e^{8 x^2} to estimate the xvalues of any ...
More Related Questions