Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on theground in such a way that the height of the cone is always one-sixth of the radius of the base.How fast is the height of the sand cone increasing when the height is 4 cm?
OR
Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to x–axis.
Since, Volume of a cone = 
And 
, r = 6h
Differentiating,
Hence, the height is increasing at the rate of 
cm/sec.
OR
Differentiating the expression,
Since the tangents are parallel to x-axis so it’s slope is 0.
X = 1
y=±2
Hence the points are (1,2) & (1,-2).
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