Question

for what value(s) of k will f(x)=x^3-kx^2+kx+k have an inflection point at x=5?

Answer 1

f(x)=x^3-kx^2+kx+k

f ' (x)=3x^2-2kx+k ... derive

f '' (x)=6x-2k ... derive again

You want the point of inflection to be at x = 5, so you want f '' (5) = 0

f '' (x)=6x-2k

f '' (5)=6*5-2k

f '' (5)=30-2k

0=30-2k

now solve for k

Answer 2

GOOD SOLVING.......