How do you find the point on the graph of #y = x^2# where the curve has a slope 5/3?

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Answer 1 · 2016-11-04T03:21:24

The point #(5/6, 25/36)#.

The curve will have an instantaneous rate of change of #5/3# when the point #x = a# is put into the derivative.

Let's start by finding the derivative.

#y' = 2x#

#5/3 = 2x#

#x = (5/3)/2#

#x = 5/6#

The corresponding y-coordinate is #y= (5/6)^2 = 25/36#.

Hopefully this helps!