Question

At which points on the curve y = 1 + 40x3 − 3x5 does the tangent line have the largest slope?

Answer 1

x = -2 and x = 2

Explanation:

By taking the derivative of the equation you get 120x^2 - 15x^4

this shows the slope of the parent function at any value of x.....then look for where the derivative graph is maximum....at x = -2 and + 2 is where the parent function has the greatest slope

Here is the graph: (red is derivative, blue is parent function)