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

1 Answer
Mike A. · Becca M.
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 xx, then substitute the x-coordinate of the point of interest in for the xx values in the derivative.

For example, if you want to know the gradient of the function y = 4x^3 - 2x^2 +7y=4x3−2x2+7 at the point (1, 9)(1,9) we would do the following:

  1. Take the derivative with respect to xx:
    12x^2 - 4x12x2−4x

  2. Substitute the x-coordinate (x=1)(x=1) in for xx:
    gradient = 12(1)^2 - 4(1) = 812(1)2−4(1)=8

So the gradient of the function at the point (1, 9)(1,9) is 88.

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