# NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 16

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**Question 21:**

Show that for is decreasing in **R**.

**Answer:**

We have,

We know that,

And

So,

Hence, is a decreasing function in R.

**Question 22:**

Show that is an increasing function in .

**Answer:**

For

Which is true, if

Hence, is an increasing function in

**Question 23:**

At what point, the slope of the curve is maximum? Also find the maximum slope.

**Answer:**

,

**Question 24:**

Prove that has maximum value at .

**Answer:**

For

Again, differentiating we get

At

Hence, at has maximum value and is the point of local maxima.