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

1 Answer
Sep 4, 2014

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#.