Application of Derivatives



Sample Paper – 2008

Class – XII

Subject - Mathematics

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Application of Derivatives

Q1 The volume of a cube is increasing at a constant rate. Prove that the increase in surface area varies inversely as the length of the edge of the cube.

Q2 Use differentials to find the approximate value of [pic]

Q3 It is given that for the function f(x) = x3 – 6x2 + ax + b on [1, 3], Rolle’s theorem holds with

c = 2+ [pic]. Find the values of a and b if f(1)= f(3) = 0

Q4 Find a point on the curve y = (x – 3)2, where the tangent is parallel to the line joining (4, 1)

and (3, 0).

Q5 Find the intervals in which the function f(x) = x4 – 8x3 + 22x2 – 24x + 21 is decreasing or increasing.

Q6 Find the local maximum or local minimum of the function.

f(x) = sin4x + cos4x, 0 ................
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