Match the graphs A, B, and C shown with the functions ƒ(x), ƒ'(x), and
Given :
The graphs of f(x) , f '(x) and Anti derivative of f(x)
First derivative test:
If f '(x)> 0 on interval (a, b) is positive then f(x) is increasing function on that interval, and
If f '(x) is negative on interval (a, b) the f(x) is decreasing on that interval.
Let R(x) be the function corresponding to red graph.
G(x) be the function corresponding to green graph, and
B(x) be the function corresponding to blue graph.
From graph see that on (-infinity, 0), the function R(x) is negative and on same interval the function B(x) is decreasing
also on (0, infinity), the function R(x) is positive and on same interval the function B(x) is increasing.
Therefore the function R(x) behaves like derivative function of B(x)
that is
R(x) = B'(x)
Step by step
Solved in 6 steps with 2 images
