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.