Application of Derivatives
The number of points in (−∞,∞),for which x2−xsinx−cosx=0,is6 (b) 4 (c) 2 (d) 0
If the function y=f(x) is represented as x=ϕ(t)=t5−5t3−20t+7, y=ψ(t)=4t3−3t2−18t+3(∣t∣<2), then find the maximum and minimum values of y=f(x)˙
Find the equation of the normal to the curve x3+y3=8xy at the point where it meets the curve y2=4x other than the origin.
A figure is bounded by the curves y=x2+1,y=0,x=0,andx=1. At what point (a,b) should a tangent be drawn to curve y=x2+1 for it to cut off a trapezium of greatest area from the figure?
Two cyclists start from the junction of two perpendicular roads, there velocities being 3um/m∈ and 4um/m∈ , respectively. Find the rate at which the two cyclists separate.