Question

A continuous differentiable function $f\left(x\right)$ is increasing in $(-\infty ,\frac{3}{2})$ and decreasing in $(\frac{3}{2},\infty )$. Then $x=\frac{3}{2}$ is

• A. point of local maxima
• B. point of local minima
• C. point of inflection
• D. None of these

Answer 1

The correct option is A

point of local maxima

Explanation for the correct answer:

Step 1: Create a rough diagram of for $f\left(x\right)$ is increasing in $(-\infty ,\frac{3}{2})$ and decreasing in $(\frac{3}{2},\infty )$

We have been given that, function $f\left(x\right)$ is increasing in $(-\infty ,\frac{3}{2})$ and decreasing in $(\frac{3}{2},\infty )$

We need to find the nature of $x=\frac{3}{2}$.

A rough diagram of the given situation would be,

From the above figure, we can say that the point $x=\frac{3}{2}$ is the point of local maxima.

Therefore, option (A) is the correct answer.