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.