2.8
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WebAssign Section Section 2.8 (Homework) MACE JOHN RANDALL MA 141, section 007, Fall 2008 Instructor: Kyle Thompson
Current Score: 17 out of 17 Due: Saturday, October 4, 2008 10:02 PM EDT Description The Derivative as a Function
The due date for this assignment is past. Your work can be viewed below, but no changes can be made. 1. [SCalcCC2 2.8.02.] 3/3 points Use the given graph to estimate the value of each derivative.
(a) f '(0) -3 (b) f '(1) 0 (c) f '(2) 1.5 (d) f '(3) 2 (e) f '(4) 0 (f) f '(5) -1.2
-3 0 1.5 2 0 -1.2
2. [SCalcCC2 2.8.18.] 4.5/4.5 points
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Section 2.8
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Let f(x) = x3. (a) Estimate the values of the following by using a graphing device to zoom in on the graph of f. Give your answers correct to one decimal place. f '(0) 0 0.0 f '(1/2) .75 0.8 f '(1) 3 3.0 f '(2) 12 12.0 f '(3) 27 27.0 (b) Use symmetry to deduce the values of the following. Give your answers correct to one decimal place. f '(-1/2) .75 0.8 f '(-1) 3 3.0 f '(-2) 12 12.0 f '(-3) 27 27.0 (c) Use the values from parts (a) and (b) to graph f '(x). (Do this on paper. Your teacher may ask you to turn in this work.) (d) Guess a formula for f '(x). (Do this on paper. Your teacher may ask you to turn in this work.) (e) Use the definition of a derivative to prove that your guess in part (d) is correct. this (Do on paper. Your teacher may ask you to turn in this work.)
3. [SCalcCC2 2.8.22.] 6/6 points You are given the following function.
Find the derivative of the function using the definition of derivative. f '(x) = 1+.5(x)^(-1/2) 1 + 1/(2sqrt(x))
State the domain of the function. (To enter or - , type INFINITY or -INFINITY.) [ [0 0 INFINITY INFINITY ) )
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Section 2.8
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State the domain of its derivative.(To enter or - , type INFINITY or -INFINITY.) ( (0 0 INFINITY INFINITY ) )
4. [SCalcCC2 2.8.24.] 1.5/1.5 points You are given the following function.
Find the derivative of the function using the definition of derivative. f '(x) = (82)/(1-9x)^2 82/(1-9x)^2
Select the domain of the function. (- , 1/9] [1/9, ) (- , 1/9) (1/9, ) (-1/9, 1/9) [-1/9, 1/9]
Select the domain of its derivative. (- , 1/9] [1/9, ) (- , 1/9) (1/9, ) [-1/9, 1/9] (-1/9, 1/9)
5. [SCalcCC2 2.8.32.] 2/2 points The graph of g is given below.
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Section 2.8
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(a) At what numbers is g discontinuous? (Select all that apply.) -2 -1 0 2 4 5
(b) At what numbers is g not differentiable? (Select all that apply.) -2 -1 0 2 4 5
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