Question

How do you find the slope of the tangent to the curve `y = 3 + 4x^2 - 2x^3` where x = a?

Answer 1

The derivative of a function is the slope of the tangent to that function.

Given
`y=3+4x^2−2x^3`

`(dy)/(dx) = 8x -6x^2`

So the slope of the tangent to the curve at `x=a` is
`8a -6a^2`