I'm supposed to sketch a graph of two functions that have the same derivative of a graph.

Question

The graph having a horizontal line on (0,4)

Answer 1

clearly,
y(0) = 4
y'(0) = 0

So, a parabola with vertex there will work:

y = 2x^2+4

or how about a cosine function?

y = 4cos(x)