Application of Derivatives
If y2=4b(x−c) and y2=8ax having common normal then (a,b,c) is (A) (21,2,0) (B) (1,1,3) (C) (1,1,1) (D) (1,3,2)
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:(i) f(x)=x2,x∈[−2,2] (ii) f(x)=sinx+cosx,x∈[0,π](iii) f(x)=4x−21x2,x∈[−2,29] (iv) f(x)=(x-1)
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.
Find the intervals in which the following functions are strictly increasing or decreasing:(a) x2+2x−5 (b) 10−6x−2x2 (c) −2x3−9x2−12x+1 (d) 6−9x−x2(e) (x+1)3(x−3)3
A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?