Question

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.

Answer 1

1. Answer: a. -7

Explanation:

`f(x)=(7)/(x)\implies f(x)=7x^(-1)\\\\f'(x)=-1\cdot 7x^(-1-1)\\.\qquad =-7x^(-2)\\\\.\qquad =-(7)/(x^2)\\\\f'(1)=-(7)/(1^2)\\\\.\qquad =\large\boxed{-7}`

2. Answer: a. 4

Explanation:

`f(x)=4x+7\\f'(x)=1\cdot4x^(1-1)+0\cdot7\\.\qquad=4\\\\f'(5)=\large\boxed{4}`

3. Answer: d. 224

Explanation:

`f(x)=12x^2+8x\\f'(x)=2\cdot12x^(2-1)+1\cdot8x^(1-1)\\.\qquad=24x+8\\\\f'(9)=24(9)+8\\.\qquad=216+8\\.\qquad=\large\boxed{224}`

4. Answer: d. 11/81

Explanation:

`f(x)=(-11)/(x)\implies f(x)=-11x^(-1)\\\\f'(x)=-1\cdot -11x^(-1-1)\\\\.\qquad=11x^(-2)\\\\.\qquad=(11)/(x^2)\\\\f'(9)=(11)/(9^2)\\\\.\qquad=\large\boxed{(11)/(81)}`

5. Answer: -10

Explanation:

s(t) = 1 - 10t

v = s'(t) = -10

s'(10) = -10