Application of Derivatives
Find the intervals in which the function f given by f(x)=4x3−6x2−72x+30is (a) strictly increasing (b) strictly decreasing
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The volume of a spherical balloon is increasing at the rate of 25 cubic centimetre per second. Find the rate of change of its surface area at the instant when radius is 5 cm.
Let I be any interval disjoint from [−1,1]. Prove that the function f given byf(x)=x+x1 is strictly increasing in interval disjoint from I.
Find the slope of the tangent to the curve y=3x4−4x at x = 4.
Find the equations of all lines having slope 0 which are tangent to the curve y=x2−2x+31.
Using differentials, find the approximate value of :327
The radius of an air bubble is increasing at the rate of 21cm/s. At what rate is the volume of the bubble increasing when the radius is 1cm?
Find the radius of a closed right cylinder of volume 100 cm3 which has the minimum total surface area.