Please help it’s due tonight whoever answers will

Ответ:

sarakiker

08.11.2021

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.

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