CPM Homework Help : CALC Problem 4-92

Find the equation of the line tangent to $f(x) = x^3 + 12x^2 + 36x-6$ at its point of inflection.

Hint:

Find the inflection point of a cubic function can be found by setting $f^{\prime\prime}(x) = 0$ or $f^{\prime\prime}(x) =$ DNE. What is the slope at that point?
What is the $y$ -value at that point?

Answer:

(show work)
$y = −12x − 70$
But your answer will probably be in point-slope form.