1. ## Linear approximation

The demand function for a product is given by

p=f(q)=30 -Öq

where p is the price per unit in dollars for q units. Use the linear approximation to approximate the the price when 224 units are demanded.
Solution: We want to approximate f(224). From

f(q) » L(q)=f(a)+f¢(a)(q-a)

and the fact that f¢(a)= a)-1/sqrt(a)
b) 1/(2sqrt(a))
c) - 1/(2sqrt(a))
d) 1/sqrt(a)

we choose a= ____________ .

From f(225)= ________ and f¢(225)= ________ we get f(224) » ______ .
Hence, the price per unit when 224 units are demanded is approximately $_________ . 2. Originally Posted by lemontea The demand function for a product is given by p=f(q)=30 -Öq where p is the price per unit in dollars for q units. Use the linear approximation to approximate the the price when 224 units are demanded. Solution: We want to approximate f(224). From f(q) » L(q)=f(a)+f¢(a)(q-a) and the fact that f¢(a)= a)-1/sqrt(a) b) 1/(2sqrt(a)) c) - 1/(2sqrt(a)) d) 1/sqrt(a) we choose a= ____________ . From f(225)= ________ and f¢(225)= ________ we get f(224) » ______ . Hence, the price per unit when 224 units are demanded is approximately$ _________ .
a = 225 of course. the second to last line kind of gave that away.

$\displaystyle f'(q) = \frac {-1}{2 \sqrt q}$ (we used the power rule here, recall that $\displaystyle \sqrt q = q^{1/2}$)

now just plug the values into the formula and calculate