Question 1(multiple choice worth 2 points) find the derivative of f(x) = 7 divided by x at x = 1.
-7
-1
1
7
question 2(multiple choice worth 2 points) find the derivative of f(x) = 4x + 7 at x = 5.
4
1
5
7
question 3(multiple choice worth 2 points) find the derivative of f(x) = 12x2 + 8x at x = 9.
256
-243
288
224
question 4(multiple choice worth 2 points) find the derivative of f(x) = negative 11 divided by x at x = 9.
11/9
81/11
9/11
11/81
question 5 (essay worth 2 points) the position of an object at time t is given by s(t) = 1 - 10t. find the instantaneous velocity at t = 10 by finding the derivative.

Question 1:

For this case we must find the derivative of the following function:

evaluated at

We have by definition:

So:

We evaluate in

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.

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:

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:

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

-10

yes. we do proportions in probabilities.