What are the points of inflection, if any, of f(x)= -14x^3 + 19x^2 - x - 2 ?

1 Answer
May 6, 2016

Points of inflection are (0.64,1.47) and (-0.21, -0.812)

Explanation:

To find points of inflection, differentiate the expression to get the gradients, and then find the points where the gradient is zero.
f(x) = -14x^3 +19x^2 - x - 2

f'(x)=-42x^2 +38x -1

for points of inflection, -42x^2+38x-1 = 0

42x^2 -38x +1 = 0

This does not factorise so use the quadratic equation x = (-b+-sqrt(b^2-4ac))/(2a)

x=(38+-sqrt(1444-168))/84

x~~(38+-35.72)/84

x~~0.64 or x~~-0.21

Substitute back into the original expression to find the values of f(x)

Points of inflection are (0.64,1.47) and (-0.21, -0.812)