10 multiple choice questions and 5 short answer questions

1.

Find the limit as h goes to 0 of the quotient of the quantity 2 times the square of the quantity x plus h, plus 4, minus the quantity 2 times x squared plus 4, and h . (5 points)

2.

Given f of x equals 5 times x minus 6 for x less than 3, equals x squared for x between 3 and 5 inclusive, and equals 2 times x plus 15 for x greater than 5 find f ‘(x) and give its domain. (5 points)

3.

Use a graphing calculator to graph f of x equals the quotient of the quantity 4 times x squared minus 1 and the quantity x squared minus 9 and then select the response which is true. (5 points)

4.

Find dy, dx for y = 3cos(x) + sec(x). (5 points)

5.

Differentiate y equals the quotient of the quantity 1 plus cosine x and the quantity 1 minus cosine x . (5 points)

6.

Which one of the following statements is false? (5 points)

7.

Is the following true or false?

the derivative with respect to x of the product of x and e raised to the x power equals the product of x times e to the x power and the quantity x plus 1 (5 points)

8.

If h(x) = f[g(x)], use the table of values for f, g, f ‘ and g ‘ to find the value of h ‘(1). (5 points)

x f(x) g(x) f ‘(x) g ‘(x)
1 3 2 2 6
2 1 8 5 7
3 7 2 7 9

9.

Determine the slope of the graph of x2 = ln(xy) at the point (1, e). (5 points)

10.

Find y’ if y = cos(x + y). (5 points)

Short Answer SHOW ALL WORK FOR FULL CREDIT

1.

The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours. (10 points)

a. Estimate the value of T′(6). Give units in your answer.
b. What is the meaning of T′(6)?

t 0 2 4 6 8 10 12 14
T 73 73 70 68 73 80 86 89

2.

(Find the values of m and b that make the following function differentiable.

the piecewise function f of x equals x cubed when x is less than or equal to one or mx plus b when x is greater than one

3.

Find f ‘(x) for f(x) = cos (5x2).

4.

Find f ‘(x) for f(x) = ln(x2 + e3x).

5.

Find dy over dx by implicit differentiation for x – y = xy.

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