The graph of f' is shown in the figure. Sketch the graph of f if f is continuous on [0,3] and f(0)=1.

Question

Answer 1

Like it's derivative, f(x) is a piecewise function:

f(x) = {0 ≤ x < 1 : 2x + 1, 1 ≤ x < 2 : x + 2, 2 ≤ x ≤ 3 : 6 – x}

The slope of each linear piece is given by the value of f’(x) on the same interval.

Desmos graph: desmos.com/calculator/od11vdjaji