Linear approximation of bus revenue

[bcahmel]

Homework Statement

If the price of a bus pass from Albuquerque to Los Alamos is set at x dollars, a bus company takes in a monthly revenue of R(x) = 1.5x − 0.01x2 (in thousands of dollars).

Suppose that x = 80. How will revenue be affected by a small increase in price? Explain using the Linear Approximation.

The Attempt at a Solution

first I took the derivative which is 1.5-0.02x. Then I plugged 80 in for x, so f'(x)=-0.1. Is this right? So the revenue will slightly decrease.

 

[lanedance]

so the linear approximation is
$$R(x) \approx R(x_0) +R'(x_0)(x - x_0)$$

 

[bcahmel]

ok, so its just like y=mx+b, sort of..

 

[Mark44]

Which is why they call it a linear approximation...

 

[bcahmel]

yes, I get it now...thanks mark44