Question

Which function is increasing?

Answer 1

The correct option is Option D: f(x)=(5)ˣ.

The function is increasing where its derivative is greater than 0.

for example, f(x) is increasing then f'(x) is greater than 0.

Here f(x) = aˣ

so the dervative of the function

d(f(x))/dx=d(aˣ)/dx

⇒f'(x)= ㏑(a)aˣ

f'(x)>0

⇒㏑(a)aˣ >0

as aˣ is always greater than 0,

⇒㏑(a)>0

⇒a>1

as ㏑(a) is greater than 0 when a >1 and is lesser than when 0<a<1.

checking all the options

Option A. f(x)=(1/5)ˣ here a =1/5<1 so, f(x) is not increasing. Option A is incorrect.

Option B: f(x)=(0.5)ˣ here a =0.5<1 so, f(x) is not increasing. Option B is incorrect.

Option C: f(x)=(1/15)ˣ here a =1/15<1 so, f(x) is not increasing. Option C is incorrect.

Option D: f(x)=(5)ˣ here a =5>1 so, f(x) is increasing. Option A is correct.

Therefore the correct option is Option D: f(x)=(5)ˣ.

Learn more about increasing function

here: brainly.com/question/1503051

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