Differentiation Problem

[alexcarr123]

I have no idea how to approach this problem:

Let f and g be differentiable functions with the following properties:

I. f(x)<0 for all x

II. g(5)=2

If h(x)=f(x)/g(x) and h'(x)=f'(x)/g(x), the g(x)=

a. 1/f'(x)
b. f(x)
c. -f(x)
d. 0
e. 2

 

[Deleted member 4993]

I have no idea how to approach this problem:

Let f and g be differentiable functions with the following properties:

I. f(x)<0 for all x

II. g(5)=2

If h(x)=f(x)/g(x) and h'(x)=f'(x)/g(x), the g(x)=

a. 1/f'(x)
b. f(x)
c. -f(x)
d. 0
e. 2

$\displaystyle h(x) \ = \ \frac{f(x)}{g(x)}$

$\displaystyle h'(x) \ = \ \frac{f'(x)}{g(x)} \ - \ \frac{f(x) \ * \ g'(x)}{g^2(x)}$

combined with other information given - what does the above equation tell you about nature of g'(x)?

what does the above information tell you about nature of g(x)?

Now choose your answer (utilizing other information provided to you in the problem statement) ......

 

[alexcarr123]

Would your equation for h'(x) mean that the function g is a constant function (making the derivative 0), and making g(x)=2?

 

[Deleted member 4993]

Would your equation for h'(x) mean that the function g is a constant function (making the derivative 0), and making g(x)=2?

Correct.

 

[alexcarr123]

Thank you so much for your help!