Exam 1

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Exam 1

1. Evaluate the function

f (x) = x^{2} + 5 x + 6

at the given values of the independent variable and simplify.

a. f(-3) b. f(x+3) c. f(-x)

2. f(-3) =

b. f(x+3) =

c. f(-x) =

2. The amount of money, A(t), in a savings account that pays 6% interest, compounded quarterly for t years, with an initial investment of P dollars, is given by

A (t) = P {(1 + \frac{0.06}{4})}^{45}

. If $2000 is invested at 6%, compounded quarterly, how much will the investment be worth after 4 years?

How much money will there be in the account at the end of 4 years?

3. Jimmy decides to mow lawns to earn money. The initial cost of his lawnmower is $250 . Gasoline and maintenance costs are $5 per lawn.

a) Formulate a function C(x) for the total cost of mowing x lawns.

b) Jimmy determines that the total-profit function for the lawnmowing business is given by P(x) = 6x-250

Find a function for the total revenue from mowing x lawns. How much does Jimmy charge per lawn?

c) How many lawns must Jimmy mow before he begins making a profit?

4. Compute the difference quotient

\frac{f (x + h) - f (x)}{h}

for the function f(x) =

- 4 x^{2} - x - 1

. Simplify your answer as much as possible.

\frac{f (x + h) - f (x)}{h} =

______

5. Use limits to compute the derivative.

f ‘ (1) i f f (x) = 3 x^{3}

f ‘ 1 =____

6. Find an equation for the tangent line to the graph of the given function at (2,16)

f (x) = 2 x^{3}

7. Differentiate.

y = 4 x^{3} - 2 x^{2} + x + 5

\frac{d y}{d x} =

8. Find an equation for the line that is tangent to the curve

y = x^{3} - 9 x

at the point (-3,0)

The equation of the tangent line is y=

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This question is taken from Math 2160 – Applied Calculus I » Fall 2021 » Exams

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