Determine point(s) on curves where the slopes of the tangent are equal

Question

Given:

f(x)= 18x^3 - 12x^2 - 30x +1

g(x) = 16x^3 - 9x^2 - 66x +3

Answer 1

Hey Anne!

Similar to your previous question, this has everything to do with the fact that the derivative of a function gives you the slope of that functions tangent line at any x.

So here, if you want to know where these two functions have the same slopes, you can take the derivative of each one (using the power rule), and then set your results equal.

It'll still take a bit of leg work form there to solve, but hopefully that gets you started in the right direction!