Tommy purchased a riding lawnmower with an original value of $2,500. If the value of the riding lawnmower decreases by $300 per
year, what should be the value of the lawnmower after five years?
A. $1,000
B. $1,300
C. $1,500
D. $ 2,200

a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.

Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is p'(x)=3x^2-9. In particular, the value we are looking for is p'(2)=3(2^2)-9=12-9=3.

If you would like to compute the equation of the tangent line, we can use the point-slope equation to get y=3(x-2)-10=3x-16

b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to p'(2)=3.

Step-by-step explanation: