find the inflection points

Question

Find the inflection points of f(x)=8x^4+110x^3−42x^2+13. (Give your answers as a comma separated list)

 

Inflection Points=_______

Answer 1

Set f''(x) = 0

 

f'(x) = 32x³ + 330x² - 84x

 

f''(x) = 96x² + 990x - 84

 

96x² + 990x - 84 = 0

 

 

Solve for x from this equation.  Then use 1st derivative test to evaluate the positives and negatives of the second derivative.