Question

What are the points of inflection, if any, of `f(x)=14x^3+32x^2-15x+4`?

Answer 1

Points of inflection involve the second derivative. This can be obtained by applying the power rule twice.

`f'(x) = 42x^2 + 64x - 15`

`f''(x) = 84x + 64`

When `f''(x) = 0`, there will be points of inflection.

`0 = 84x + 64`

`x = -16/21`

Hence, there will be a point of inflection when `x = -16/21`. Here is a graphical representation of the given function.

Hopefully this helps!