diffrentiation

hello there
i am very much troubled by this sum,its just getting difficult
please help me out

The radius,r cm, of a circle at time t seconds is given by r= 2t^2 +1. Express its area ,A cm^2, in terms of t and find the rate of change of area at the instant when t=2

Thank you very much

Thank you very much

diffrentiation

Hello Emile
Welcome To MyTutorOnline
Problem is very simple,you too will agree with this soon
we have
Radius of circle at tim t

r(t)= 2t^2+1
As area of circle is Pie*radius*radius
so putting the radius value we have
A(t)=Pi(r^2)
=Pi(2t^2+1)^2
= Pi( 4t^4+4t^2+1)
To find the rate of change of area we have to diffretiate it so we have

the rate of change of area is A'(t)= Pi(16t^3+8t)
we have to find Value to rate of change at t=2 so put its value
A'(t=2)= Pi(16* 2^3 +8*2
A'(t=2)= Pi(144)

answer

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