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

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

1 answer

a) 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
Similar Questions
  1. Given the function: f(x) = x^2 + 1 / x^2 - 9a)find y and x intercepts b) find the first derivative c) find any critical values
    1. answers icon 1 answer
  2. Given the function: f(x) = x^2 + 1 / x^2 - 9a)find y and x intercepts b) find the first derivative c) find any critical values
    1. answers icon 0 answers
  3. R(x)=x^2+x-6________ x-3 1. find the domain and y-intercepts 2. find the x-intercepts 3. find the real solution of the equation
    1. answers icon 1 answer
  4. Please help!!*f(x)= x(x+6)^1/2 find two x intercepts. Then show that f'(x)=0 at some point between the 2 x intercepts. *Use mean
    1. answers icon 3 answers
more similar questions