Application of Derivatives
A particle is projected with a velocity of 39.2 m/sec at an elevation of 30°. Find(i) the time of flight.(ii) the greatest height.
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:(i) f(x)=x2 (ii) g(x)=x3−3x (iii) h(x)=sinx+cosx,0<x<π2 (iv) f(x)=sinx−cosx,0<x<2π(v)f(x) = x3−6x2+9x+15(vi) g(x) =2x+x2 , x>0(vii) g(x) = x2+21(viii) f(x)=x1−x , x>0
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?
Show that the normal at any point θto the curvex=acosθ+aθsinθ,y=asinθ−aθcosθis at a constant distance from the origin.
Find the least value of a such that the function f given by f(x)=x2+ax+1is strictly increasing on (1,2)˙
Manufacturer can sell x items at a price of rupees (5−100x)each. The cost price of x items is Rs (5x+500). Find the number of items he should sell to earn maximum profit