Class 12

Math

Calculus

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.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

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) $f(x)=x_{2}$ (ii) $g(x)=x_{3}−3x$ (iii) $h(x)=sinx+cosx,0<x<π2$ (iv) $f(x)=sinx−cosx$,$0<x<2π$(v)f(x) = $x_{3}−6x_{2}+9x+15$(vi) g(x) =$2x +x2 $ , $x>0$(vii) g(x) = $x_{2}+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 $θ$to the curve$x=acosθ+aθsinθ,$$y=asinθ−aθcosθ$is at a constant distance from the origin.

Find the least value of a such that the function f given by $f(x)=x_{2}+ax+1$is strictly increasing on $(1,2)˙$

Show that the function given by $f(x)=7x3$is strictly increasing on R.

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

Find the equations of all lines having slope 0 which are tangent to the curve $y=x_{2}−2x+31 $.

The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C(x)=0.005x_{3}−0.02x_{2}+30x+5000$. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.