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NCERT Class 12- Mathematics: Chapter β 6 Application of Derivatives Part 16
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.