Question

f(x)=0.1x^4-3.2x+7
Use derivatives to find the x-coordinates of all critical points

I got 0=0.4(x^3-8)
I know that means 0=0.4 and 0=x^3-8. Does that mean 0=0.4 is undefined?

Answer 1

f'(x) = 0.4x^3 - 3.2 let it = 0
0.4x63 -3.2 = 0
or
0.4x^3 = 3.2

x^3 = 8

then the stationary points are at x = 2 thats the only one

f"(x) = 1.2x^2 test x= 2 f"(x) >0 therefore at x = 2 there is a minimum

Answer 2

I think you'll find there is a point of inflexion at x = 0... found by solving the 2nd derivative

Answer 3

Thank you!!!! :)