AP Calculus BC : Graphs of f and f'

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

Example Question #1 : Graphs Of F And F'

Assuming f(x) is continuous and differentiable for all values of x, what can be said about its graph at the point  if we know that  ?

Possible Answers:

f(x) is increasing when 

f(x) is decreasing when 

There is not sufficient information to describe f(x).

f(x) is concave up when 

Correct answer:

f(x) is increasing when 

Explanation:

Assuming f(x) is continuous and differentiable for all values of x, what can be said about its graph at the point  if we know that  ?

 

We are told about a first derivative and asked to consider the original function. Recall that anywhere the first derivative is negative, the original function is decreasing. Anywhere the first derivative is positive, the original function is increasing.

We are told that . In other words, the first derivative is positive.

This means our original function must be increasing.

f(x) is increasing when 

 

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