Question

Which of the following is a monotonically decreasing function?

• A. f(x) = ln (x)
• B. $f\left(x\right)=3-x^3$
• C. $f\left(x\right)=e^x$
• D. $f\left(x\right)=\frac{1}{x^2}$

Answer 1

The correct option is B

$f\left(x\right)=3-x^3$

For a monotonically decreasing function $f^{\prime }\left(x\right)\le 0$

a. f(x) = ln(x) we know that the domain of ln(x) is all positive real numbers (x> 0).

f’(x) = $\frac{1}{x}$

If we put positive real numbers f’(x) will always be positive. The function ln(x) is a strictly increasing function.

b. $f\left(x\right)=3-x^3$

$f^{\prime }\left(x\right)=-3x^2$

f’(x) will always be a non -positive number. It can’t be positive.

So, f(x) is a monotonically decreasing function.

So the correct answer is b