How to sketch the graph of a differntiable function y = f(x) that has the given properties.Local minimum at (1,1) and local maximum at (3,3)

Answer 1

polynomials are nice differentiable functions.

f'(x) = a(x-1)(x-3)
f(x) = a/3 x(x-3)^2 + b

f(3) = 3 = b
f(1) = 1 = 4a/3 + b = 4a/3+3, so a = -1/2

f(x) = -1/2 x(x-3)^2 + 3