# NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 2

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**Question 2:**

Water is dripping out from a conical funnel of semi-vertical angle at the uniform rate of the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is , find the rate of decrease of the slant height of water.

**Answer:**

If *s* represents the surface area, then

Therefore,

When

**Question 3:**

Find the angle of intersection of the curves and *.*

**Answer:**

Solving the given equations, we have and

Therefore,

i.e. points of intersection are and

Further

And

At , the slope of the tangent to the curve is parallel to axis and the tangent to the curve is parallel to axis.

Angle of intersection and that of is .

**Question 4:**

Prove that the function is strictly decreasing on

**Answer:**

When

Therefore,

Thus for

Hence is strictly decreasing on .

**Question 5:**

Determine for which values of *x*, the function is increasing and for which values, it is decreasing.

**Answer:**

Now,

Since and is continuous in and. Therefore is decreasing in and is increasing in.

**Note**: Here *f* is strictly decreasing in and is strictly increasing in .

**Question 6:**

Show that the function has neither maxima nor minima.

**Answer:**

Hence is a point of inflexion i.e. neither a point of maxima nor a point of minima.

is the only critical point, and has neither maxima nor minima.

**Question 7:**

Using differentials, find the approximate value of

**Answer:**

Let

Using *.* , taking and , we get