Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Price before membership= price 1 = $6
price after membership = price 2 = $4
Membership price = $100
SO according to price 1 and price 2; price after membership saves up $2 for each session.
Hence to justify the price of membership number of sessions can be calculated as follows:-
$2 saved = 1 session
to make it $100 multiply both sides by 50
2×50 = 1×50
100$ saved = 50 sessions
so 50 sessions ate required to justify buying the membership.
Hope this helped :)
Actually,I believe it is the rule of 72
72/4.5 = 16 years
