Application of Derivatives
Find the intervals in which the function f given by f(x)=2x2−3xis(a) strictly increasing (b) strictly decreasing
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If a>b>0, with the aid of Lagranges mean value theorem, prove that nbn−1(a−b)1.
Using Lagranges mean value theorem, prove that ∣cosa−cosb∣≤∣a−b∣˙
Draw the graph of f(x)=x2−xx2−5x+6
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
Find the equation of the normal to the curve y=∣∣x2−∣∣x∣∣atx=−2.
If in a triangle ABC,
the side c
and the angle C
remain constant, while the remaining elements are changed slightly, show that
Discuss the extremum of f(x)=x(x2−4)−31
If the tangent at (1,1)
meets the curve again at P,
then find coordinates of P˙