find the inflection points of x^4+5x^3-9x^2+6

Answer 1

An inflection point is where the second derivative of a function changes sign, also where curvature changes from concave to convex or vice versa.

Therefore to find inflection points, we only need to equate the second derivative of a function to zero, and solve for the zeroes.

f(x)=x^4+5x^3-9x^2+6
f"(x)=12x^2+30x-18
So solve for x where f"(x)=0.
Can you take it from here?