# #f'(x)>0# for all x. Can you use the quotient rule to show that #1/f(x)# is monotonically decreasing?

##### 1 Answer

Feb 14, 2016

Yes you can

#### Explanation:

#frac{d}{dx}(1/f(x)) = frac{f(x)frac{d}{dx}(1)-(1)frac{d}{dx}(f(x))}{f(x)^2}#

#= -frac{f'(x)}{f(x)^2}#

Since

#frac{d}{dx}(1/f(x)) = -frac{f'(x)}{f(x)^2} < 0#

for all

Therefore,