Application of Derivatives
Find the rate of change of the area of a circle with respect to its radius r when(a) r=3cm (b) r=4cm
Find the value of n∈N such that the curve (ax)n+(by)n=2 touches the straight line ax+by=2 at the point (a,b)˙
At the point P(a,an) on the graph of y=xn,(n∈N) , in the first quadrant, a normal is drawn. The normal intersects the y−aξs at the point (0,b) . If (lim)a0=21, then n equals _____.
A private telephone company serving a small community makes a profit of Rs. 12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise per subscriber. Thus, there will be profit of Rs. 11.99 on each of the 726 subscribers, Rs. 11.98 on each of the 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit?
Let f(x)=2x3=9x2+12x+6. Discuss the global maxima and minima of f(x)∈[0,2]and(1,3) and, hence, find the range of f(x) for corresponding intervals.
A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/m∈ . When the thickness of ice is 5cm, then find the rate at which the thickness of ice decreases.