Question

How do you find the slope and tangent line to the graph `y= -3x^5-8x^3+4x^2` at x=1?

Answer 1

First you need the slope `m` that you get deriving your function and substituting `x=1` in it. Then you find the coordinates (`x_0,y_0`) of the point of tangency by substituting `x=1` in your original function. And finally use the expression:
`y-y_0=m(x-x_0)` to find the equation of the tangent line.

And graphically: