Question

How do you find the gradient of a function at a given point?

Answer 1

The gradient of a function is also known as the slope, and the slope (of a tangent) at a given point on a function is also known as the derivative.

To find the gradient, take the derivative of the function with respect to `x`, then substitute the x-coordinate of the point of interest in for the `x` values in the derivative.

For example, if you want to know the gradient of the function `y = 4x^3 - 2x^2 +7` at the point `(1, 9)` we would do the following:

1. Take the derivative with respect to `x`:
   `12x^2 - 4x`

2. Substitute the x-coordinate `(x=1)` in for `x`:
   gradient = `12(1)^2 - 4(1) = 8`

So the gradient of the function at the point `(1, 9)` is `8`.