Exam 11: Mathematical Functions and Limits

If an object moves along a line so that it is at y = f(x) = 10x² at time x (in seconds), find the velocity at x =1 (y is measured in feet).

Find the equation of the tangent line at x = 7 for f(x) = Write the answer in the form y = mx +b.

Find f'(x) for f(x) =

Determine the limit.

f(x) =

A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: 0 c x c 100 Find the marginal cost at a production level of 70 dozen pens and interpret the result.

Find f'(x) if f(x) =

Find y' if y = 6x.

A company is planning to manufacture a new blender.After conducting extensive market surveys,the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per blender.Assuming the demand equation is linear,use the research department's estimates to find the revenue equation in terms of the demand x.

Suppose the demand for a certain item is given by D(p) = where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

Let f and g be functions that satisfy f'(4)= 2 and g'(4)= -3.Find h'(4)for h(x)= 3f(x)- g(x)+ 2.

Find: lim x·- 4

y=

The cost of renting a snowblower is $20 for the first hour (or any fraction thereof)and $5 for each additional hour (or fraction thereof)up to a maximum rental time of 5 hours.Write a piecewise definition of the cost C(x)of renting a snowblower for x hours.Is C(x)continuous at x = 2.5?

Use the four step process to find f'(x) for the function .