Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

For what values of x is #f(x)=(x-1)(x-6)(x-2)# concave or convex?

↳Redirected from "How do you find the area of the region bounded by the polar curves #r=1+cos(theta)# and #r=1-cos(theta)# ?"

1 Answer

Feb 20, 2017

See below.

Explanation:

#f(x) = (x-1)(x6)(x-2) = x^3-9x^2+20x-12#

#f'(x) = 3x^2-18x+20#

#f''(x) = 6x-18#

#f''(x)# is negative for #x < 3#, so #f# is concave (or concave down) on #(-oo,3)#.

#f''(x)# is positive for #3 < x#, so #f# is convex (or concave up) on #(3,oo)#.

Related questions

See all questions in Analyzing Concavity of a Function

Impact of this question

1675 views around the world

You can reuse this answer
Creative Commons License