Question 1:
For this case we must find the derivative of the following function:
evaluated at
We have by definition:
So:
We evaluate in
ANswer:
Option A
Question 2:
For this we must find the derivative of the following function:
We have by definition:
The derivative of a constant is 0
So:
Thus, the value of the derivative is 4.
Answer:
Option A
Question 3:
For this we must find the derivative of the following function:
We have by definition:
So:
We evaluate for we have:
Answer:
Option D
Question 4:
For this we must find the derivative of the following function:
We have by definition:
So:
We evaluate for and we have:
ANswer:
Option D
Question 5:
For this case we have by definition, that the derivative of the position is the velocity. That is to say:
Where:
s: It's the position
v: It's the velocity
t: It's time
We have the position is:
We derive:
So, the instantaneous velocity is -10
Answer:
-10