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.

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

2. Answer: a. 4

Step-by-step explanation:

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

3. Answer: d. 224

Step-by-step explanation:

[tex]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}[/tex]

4. Answer: d. 11/81

Step-by-step explanation:

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

5. Answer: -10

Step-by-step explanation:

s(t) = 1 - 10t

v = s'(t) = -10

s'(10) = -10