Question

Find numbers a and b such that the graph of the function f(x)= ax^3+bx^2 passes through (-1,1) and has an inflection point at x=1/2

Answer 1

Hello,

Explanation:

f(x) passes through (-1,1):

-a+b=1

f(x) has an inflection point at x=1/2:

f''(x)=6ax+2b

f''(1/2)=0 => 3a+2b=0

So b=-3a/2 and -a-3/2a=1

a=-2/5 and b=3/5