1a)Find a linear approximation to the function f(x)=x^(1/2) that agrees with this function at x=4

and at x=9

y=_________________

b) Use this approximating function to find the approximate value of 4.5^(1/2)

__________

c) and 5^1/2)

_______________

2)The area of a square whose sides have length 3+x is given by the function A(x)=(3+x)^2

Thus A(0) is the area of a square with sides of length 3. The function f(x)=9+6x

is a linear approximation to A(x).What is the error in this approximation when x=0.1?

____________

3)A rectangle initially has width 9 meters and length 9 meters and is expanding so that the area increases at a rate of 8 square meters per hour. If the width increases by 20 centimeters per hour how quickly does the length increase initially? [hint: Using the product rule, if you know any two of the derivatives you can work out the third one. Here you know A=L*W and A' and W'.]

_______________centimeters per hour