Question

List corresponding features of the graphs of a function f, its first derivative f′, and (an) antiderivative F. Describe a strategy whereby, given a plot showing the graphs of f, f′, and F, you can determine which is which. Apply your strategy to identify the graphs A (blue), B (red) and C (green) as the graphs of a function f, its first derivative f′, and (an) antiderivative F:


is the graph of the function f.


is the graph of the function's first derivative f′.


is the graph of an antiderivative of the function F.

Answer 1

For example:

$f(x)=2x, f'(x)=2, F(x)=x^2$

For the given graphs:

f(x) is a line with slope=2

f'(x) is a line parallel to-x-axis

F(x) is a parabola with vertex in the origin

Strategy: we can determine which graph is for which function (in our case) by degree of function:

f(x) is of the 1st degree, f'(x) is a constant, F(x) is of the 2nd degree.