Question

Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)?

Answer 1

Find the second derivative (apply the power rule twice).

`f'(x) = 3x^2 - 6x + 21`

`f''(x) = 6x- 6`

This will have an inflection point when `f''(x) = 0`.

`0 = 6x- 6`

`6 = 6x`

`x = 1`

I will leave it up to you as an exercise to figure out the concave up and concave down intervals. Just recall that if `f''(x) > 0`, then the graph is concave up and when `f''(x) < 0` it's concave down.

Hopefully this helps!