Question

For every value of x, the function f(x) = `1/7^x` is ______ 

Options

• Decreasing

• Increasing

• Neither increasing nor decreasing

• Increasing for x > 0 and decreasing for x < 0

Answer 1

For every value of x, the function f(x) = `1/7^x` is Decreasing.

Explanation:

f(x) = 7^-x

∴ f'(x) = `-7^-x log_e 7`

= `-(log_e7)/(7^x)`

 ⇒ f'(x) < 0 for all x

i.e., f(x) is decreasing for all x.