I can't seem to get the answer. Will You please help me answer this question. I am studying for a test.
"If a new car is valued at $21000 and 10 years later it is valued at $3000, then what is the average rate of change of its value during those 10 years?"
The Average Rate of Change of a function f(x) between x = x1 and x = x2 is defined as:
Δy/Δx = (f(x2) - f(x1))/(x2 - x1). [See any precalculus or calculus I text.]
For this question:
Δy/Δx = (3000 - 21000)/(10 - 0) = –18000/10 = –$1800/year.
Δy/Δx is the slope of the Secant Line between P1 and P2. If P2 is moved along the function graph closer and closer to P1, the secant line they define will approach the tangent line at P1. The slope of the tangent line is the slope of the function at P1 and the derivative of f at P1.