Application of Derivatives
A value of C for which the conclusion of Mean Value Theorem holds for the function f(x)=(log)exon the interval [1, 3] is
If the tangent to the curve xy+ax+by=0 at (1,1) is inclined at an angle tan−12 with x-axis, then find aandb?
An electric light is placed directly over the centre of a circular plot of lawn 100 m in diameter. Assuming that the intensity of light varies directly as the sine of the angle at which it strikes an illuminated surface and inversely as the square of its distance from its surface, how should the light be hung in order that the intensity may be as great as possible at the circumference of the plot?
If water is poured into an inverted hollow cone whose semi-vertical angel is 300, show that its depth (measured along the axis) increases at the rate of 1 cm/s. Find the rate at which the volume of water increases when the depth is 24 cm.
The acute angle between the curves y=∣∣x2−1∣∣and y=∣∣x2−3∣∣ at their points of intersection when when x> 0, is
A sheet of area 40m2 is used to make an open tank with square base. Find the dimensions of the base such that the volume of this tank is maximum.
Water is dropped at the rate of 2 m3/s into a cone of semi-vertical angle is 45∘ . If the rate at which periphery of water surface changes when the height of the water in the cone is 2m is d. Then the value of 5d is _____ m/sec