Application of Derivatives
The function f(x)=tan−1(sinx+cosx)is an increasing function in
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is (a32+b32)23 .
The curve f(x)=x−10x2+ax+6 has a stationary point at (4,1) . Find the values of aandb . Also, show that f(x) has point of maxima at this point.
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?
Let C be a curve defined by y=ea+bx2˙ The curve C passes through the point P(1,1) and the slope of the tangent at P is (−2)˙ Then the value of 2a−3b is_____.