Consider the following function. Graph the function. (Do this on paper. Your instructor may ask you to to turn in this work.)

What symmetries, if any, does the graph have? (Select all that apply.)

Specify the interval over which the function is increasing. (If you need to enter or -, type INFINITY or -INFINITY.)
2 ? ( [

Answer is not case sensitive.

3,

Enter a number.

4 5 ? ) ]
Specify the interval over which the function is decreasing. (If you need to enter or -, type INFINITY or -INFINITY.)
6 ? ( [

Enter a number.

7,

Answer is not case sensitive.

8 9 ? ) ]

Ohm's law for electrical circuits like the one shown in the accompanying figure states that V = RI. In this equation, V is a constant voltage, I is the current in amperes, and R is the resistance in ohms. Your firm has been asked to supply the resistors for a circuit in which V will be 120 volts and I is to be 5 0.1 amp. In what interval does R have to lie for I to be within 0.1 amp of the value I₀ = 5?

Enter a number.

1 < R <

Enter a number.

2

Using the definition, calculate the derivative of the function below, then find the values of the derivatives as specified.

f '(x) =	Enter a mathematical expression. 1
f '(-5) =	Enter a number. 2
f '(0) =	Enter an exact number. 3
f '(3) =	Enter a number. 4

(a) Find the derivative f '(x) of the given function y = f(x).

Enter a mathematical expression.

1
(b) Graph y = f(x) and y = f '(x) side by side using separate sets of coordinate axes, and answer the following questions.

(c) For what values of x, if any, is f ' positive? (Select all that apply.)

For what values of x, if any, is f ' zero? (Select all that apply.)

For what values of x, if any, is f ' negative? (Select all that apply.)

(d) Over what intervals of x-values, if any, does the function y = f(x) increase as x increases? (Select all that apply.)

Over what intervals of x-values, if any, does the function y = f(x) decrease as x increases? (Select all that apply.)

Find the derivative at each critical point and determine the local extreme values. Where are the critical points?
x =

Enter a number.

1 (smallest value)
x =

Enter an exact number.

2
x =

Enter a number.

3 (largest value)
What are the derivatives at these points? (If they do not exist, enter DNE.)

Answer is not case sensitive.

4

Answer is not case sensitive.

5

Answer is not case sensitive.

6
What are the values at these points?
y =

Enter a number.

7
y =

Enter an exact number.

8
y =

Enter a number.

9