APPLICATION OF DERIVATIVES

APPLICATION OF DERIVATIVES
TWO/THREE/FIVE MARK QUESTIONS:
1) Find the rate of change of the area of a circle w.r.t to its radius ‘r’
when r = 4 cm?
Ans: Area of circle A = r
2
, dA/dr = ? when r = 4 cm
Differentiate w.r.t. ‘r’
dA/dr = (2r)
= (2)(4)
= 8 sq. cms
Therefore area of the circle is increasing at the rate of 8 sq. cms.
2) An edge of a variable cube is increasing at the rate of 3cm/s. How fast is
the volume of the cube increasing when the edge is 10cm long?
Ans: Volume of a cube V = x
3
., Given: dx/dt = 3cm/s. dV/dt = ?
when x = 10cm
Didifferentiate w.r.t ‘t’
dV/dt = 3x
2
(dx/dt)
= 3(10)
2 . (3)
= 900 c.c/s
Therefore volume of the cube increasing at the rate of 900 c.c/s.