Find k if the tangent to y=2x^3+kx^2-3 at the point where x=1 has a slope of 2.

Answer 1

Hey Marie,

For this question, our big idea is that the derivative of a given function can tell us the slope of the tangent line at any x value.

So if we take the derivative of our function with respect to x we get:

y' = 6x²+ 2kx

So this is basically a new formula we can use. If we plug in any x and evaluate, the output will be the slope of the tangent line to our original function at that point. So now we go back to the questions. We know that when x = 1, the slope is 2. This means when I plug 1 in for x in that derivative function, I need to get out 2!

This lets us do the following:

2 = 6(1)² + 2k(1).

Now you're on the the home stretch. Just some simple algebra the rest of the way to solve for k. If you have any questions, feel free to reach out.