Given $f ( 3 ) = 5 , f ^ { \prime } ( 3 ) = 1.1 , g ( 3 ) = - 4 \text { and } g ^ { \prime } ( 3 ) = 0.7 \text {, find the value of } ( f / g ) ^ { \prime } ( 3 ) \text {. }$
A)0.025
B)0.49375
C) $- 0.49375$
D) $- 0.025$

E)1.975
F) $- 1.975$
G)0.5625
H) $- 0.5625$

Question

Given $f ( 3 ) = 5 , f ^ { \prime } ( 3 ) = 1.1 , g ( 3 ) = - 4 \text { and } g ^ { \prime } ( 3 ) = 0.7 \text {, find the value of } ( f / g ) ^ { \prime } ( 3 ) \text {. }$
A)0.025
B)0.49375
C) $- 0.49375$ 
D) $- 0.025$

E)1.975
F) $- 1.975$
G)0.5625
H) $- 0.5625$

Quizplus · Accepted Answer

Using the quotient rule: $(f/g)' = (f'g - fg')/g^2$. Plugging in the values: $(1.1 \times -4 - 5 \times 0.7)/(-4)^2 = (-4.4 - 3.5)/16 = -7.9/16 = -0.49375$.

Given A)0025 B)0 −0.49375- 0.49375−0.49375 D) −0.025- 0.025−0.025 E)1975 F) −1.975- 1.975−1.975 G)05625 H)

Given A)0025
B)0 $- 0.49375$ D) $- 0.025$ E)1975
F) $- 1.975$ G)05625
H)