Question

Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.

Answer 1

1. Answer: a. -7

Step-by-step explanation:

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

2. Answer: a. 4

Step-by-step explanation:

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

3. Answer: d. 224

Step-by-step 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

Step-by-step explanation:

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

5. Answer: -10

Step-by-step explanation:

s(t) = 1 - 10t

v = s'(t) = -10

     s'(10) = -10