AP Calculus AB : Corresponding characteristics of graphs of ƒ and ƒ'
Study concepts, example questions & explanations for AP Calculus AB
All AP Calculus AB Resources
Example Questions
Example Question #1 : Conceptualizing Derivatives
The speed of a car traveling on the highway is given by the following function of time:
Consider a second function:
What can we conclude about this second function?
It represents another way to write the car's speed.
It represents the change in distance over a given time 
It represents the total distance the car has traveled at time 
It represents the rate at which the speed of the car is changing.
It has no relation to the previous function.
It represents the rate at which the speed of the car is changing.
Notice that the function 
Therefore, 
Example Question #2 : Derivative As A Function
Find the critical numbers of the function,
1) Recall the definition of a critical point:
The critical points of a function 
2) Differentiate 
3) Set to zero and solve for 
The critical numbers are,
We can also observe that the derivative does not exist at 
Further Discussion
In this problem we were asked to obtain the critical numbers. If were were asked to find the critical points, we would simply evaluate the function 
Example Question #2 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'
The function 
If the following are true:
Which function could be 
To answer this problem we must first interpret our given conditions:
-
Implies the function is strictly increasing.
-
Implies the function is strictly concave down.
We note the only function given which fufills both of these conditions is 
Example Question #2 : Derivative As A Function
A jogger leaves City 
where 
Find the acceleration of the jogger at 
The accelaration is given by the second derivative of the position function:
For the given position function:
Therefore, the acceleration at 
Certified Tutor
All AP Calculus AB Resources
