NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 15
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Question 18:
At what points on the curve, the tangents are parallel to the axis?
Answer:
Given, equation of curve which is
Since, the tangents are parallel to the
For from Eq. (ii), we get
So, the require points are
Question 19:
Show that the line , touches the curve at the point where the curve intersects the axis of .
Answer:
We have the equation of line given by , which touches the curve
So, slope point of intersection on the curve with
Now, slope of the given line at is given by
Also, the slope of the curve at is
Since,
Hence, the line touches the curve at the point, where the curve intersects the axis of
Question 20:
Show that is increasing in
Answer:
We have,
For increasing function,
Which is true for any real value of .
Hence, is increasing in R.