Question

What function is increasing? will give brainlist !

Answer 1

Answer:

Option B.

Step-by-step explanation:

Option A.

f(x) = $(0.5)^{x}$

Derivative of the given function,

f'(x) = $\frac{d}{dx}(0.5)^x$

      = $(0.5)^x[\text{ln}(0.5)]$

      = $-(0.693)(0.5)^{x}$

Since derivative of the function is negative, the given function is decreasing.

Option B. f(x) = $5^x$

f'(x) = $\frac{d}{dx}(5)^x$

      = $(5)^x[\text{ln}(5)]$

      = $1.609(5)^x$

Since derivative is positive, given function is increasing.

Option C. f(x) = $(\frac{1}{5})^x$

f'(x) = $\frac{d}{dx}(\frac{1}{5})^x$

      = $\frac{d}{dx}(5)^{(-x)}$

      = $-5^{-x}.\text{ln}(5)$

Since derivative is negative, given function is decreasing.

Option D. f(x) = $(\frac{1}{15})^x$

                f'(x) = $-15^{-x}[\text{ln}(15)]$

                       = $-2.708(15)^{-x}$

Since derivative is negative, given function is decreasing.

Option (B) is the answer.