Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions.

Question

c) f'(-3) = 0 and f'(1) = 0

Please show me, step by step, how to sketch the problem!

Answer 1

There is more than one solution to this problem. Try an polynomial equation of with a derivative that must satsify the two zero points:
f'(x) = (x+3)(x-1) = x^2 +2x -3
f(x) = x^3/3 + x^2 -3x + (any constant)

Note that there is an arbitrary constant, so there are already an infinite number of functions. I could just as well have picked a cosine function f(x) = cos (a*pi*x) with zero slope
f'(x) = - a pi sin a*pi*x = 0
at integer values of x, with a being any integer
(ax = n*pi)

We can't draw graphs for you. You can do that.