How do you graph the derivative of #f(x) = x^2#?

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Answer 1 · 2016-02-13T17:53:03

Plot y = 2x, so it will be a straight line, passing through the origin with a gradient of 2.

Plot y = 2x, so it will be a straight line, passing through the origin with a gradient of 2.

The derivative of f(x) is:
f'(x) = 2x

Answer 2 · 2016-02-13T17:53:45

#f'(x)=2x# and is hence a linear graph so a straight line of slope #2# and intercept #(0,0)#.

The derivative of any function at any point represents the gradient of the tangent of that function at the point.

The derivative of this particular quadratic function is #d/dxx^2=2x#.

This represents a linear function and hence a straight line graph of gradient 2 and intercept the origin.
It is hence drawn as follows :

graph{2x [-11.25, 11.25, -5.625, 5.625]}