251 Test 2 Review PDF

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Review Test 2 for MTH251...

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Math 251 – Calculus 1 Fall 2017 – Selph Review Objectives for Test 2: Sections 2.3-2.6, 3.1-3.3 You may use a calculator (no symbolic calculators or cell phones) for the entire test. For the second test, you should be able to: Define the derivative function, and use the definition of the derivative f (x + h) − f (x) to differentiate a function. f "(x) = lim h →0 h

Objective 1:

Exercises: Use the definition of the derivative to differentiate a) g(x) = 5 − 6 x and b) y = x 3 − 3 . Chapter 2 Review Exercises: p. 117 #22 Objective 2: Given the graph of a function, sketch a reasonable graph of its derivative. Exercise: Chapter 2 Review Exercises: p. 116 #13, 15, 17 Objective 3:

Use and interpret the language and notation of derivatives, including Leibniz notation.

Objective 4: Sketch the graph of a function that satisfies given properties involving the function itself and its derivative. Exercise: Chapter 2 Review Exercises: p. 119 #52 Objective 5: Interpret the meaning of the first derivative in an application setting, including determination of the units on the derivative function. Exercises: Chapter 2 Review Exercises: pp. 118-119 #41, 42, 54, 55 Objective 6:

Understand the second derivative concept and its graphical interpretation.

Objective 7: Interpret velocity as the derivative of a position function and acceleration as the derivative of a velocity function. Exercise: Chapter 2 Review Exercises: p. 120 #62 Objective 8: Graphically and symbolically determine points where a function is discontinuous and points where a function is not differentiable. (Review Section 2.6.) Objective 9: Find derivatives of functions using the constant multiple rule, the sum and difference rules, and the power rule. (Review Section 3.1.) Objective 10: Find derivatives of exponential functions. (Review Section 3.2.) Objective 11: Find derivatives of functions using the product and quotient rules. (Review Section 3.3.) Objective 12: Find the equation of a line tangent to a curve at a given point. Exercises: 3.1 #60; 3.3 #46

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Objective 13: Analyze a function using calculus techniques including: identifying intervals of increase/decrease and identifying intervals where the function is concave up/concave down. (We used sign charts in class to help us analyze functions.) Exercises: 3.1 #62; 3.3 #43 Also spend some time reviewing homework problems and workshop problems in preparing for this test.

Answers: (Answers to odd-numbered review problems are in the back of the text.) Obj. 1, a) g"(x) = −6 Obj. 5, p. 118 #42)

b)

dy = 3x 2 dx

p. 117 #22) f ! (x) =10x +1

f (6) ≈ 44.1 million people, f ! (6) ≈ −0.27 million people per year

p. 119 #54) a) f ! (t) is negative because temperature is decreasing. b) degrees per minute Obj. 7, p. 120 #62) a) IV b) III c) II d) I e) IV f) II Obj. 13, 3.1 #60) y =

3.3 #46) y = Obj. 14, 3.1 #62)

28 19 x− 3 3 15 21 x+ 144 144

(−∞, 0 ) ∪ (2, 3)...