For #1-2, find the derivative of the function
4) The equation of the tangent line to the curve [pic] at the point (1, 7) is
(a) [pic] (b) [pic] (c) [pic]
(d) [pic] (e) [pic]
7) If the line [pic] is tangent to the curve [pic], then c is
(a) 2 (b) 4 (c) 7 (d) 11 (e) 15
32) At what point on the curve [pic] is the tangent line vertical?
(a) (0, 0) only (b) (-1, 0) only (c) [pic] only
(d) (-1, 0) and (0, 0) (e) The tangent line is never vertical.
39) Let f and g be functions that are differentiable for all real numbers x with [pic]. If [pic] is an equation of the line tangent to the graph of f at [pic], what is the equation of the line tangent to the graph of y at [pic]?
(a) [pic] (b) [pic] (c) [pic] (d) [pic] (e) [pic]
43) Let f be the function given by [pic]. The tangent line to the graph at [pic]is used to approximate [pic]. What is the error in this approximation?
(a) 0 (b) 0.008 (c) 0.248 (d) 0.400 (e) 0.648
45) Find the y-intercept of the line tangent to [pic] at [pic].
(a) -21.032 (b) -2.081 (c) 0 (d) 4.161 (e) 21.746
23) The curve [pic] passes through (3, 0). Use local linearization to estimate the value of y at [pic]. The value is
(a) -2.7 (b) -0.9 (c) 0 (d) 0.1 (e) 3.0
10) An equation of the line tangent to [pic] at [pic] is
(a) [pic] (b) [pic]
(c) [pic] (d) [pic]
(e) [pic]
17) Find the equation of the tangent line to [pic] through (2, -1).
(a) [pic] (b) [pic] (c) [pic] (d) [pic]
(e) [pic]
8) An equation of the line normal to [pic] at (2, 4) is
(a) [pic] (b) [pic] (c) [pic]
(d) [pic] (e) [pic]
13) The slope of the line tangent to the graph of [pic] at (2, 1) is
(a) [pic] (b) [pic] (c) [pic] (d) 12 (e) -7
22) Find the slope of the normal line to [pic] at (0, 1).
(a) 1 (b) -1 (c) 0 (d) 2 (e) undefined
40) Which of the following is an equation of the line tangent to the graph of [pic] at [pic]?
(a) [pic] (b) [pic] (c) [pic] (d) [pic]
(e) [pic]
12) What is the equation of the line tangent to the graph of [pic] at [pic]?
(a) [pic] (b) [pic] (c) [pic]
(d) [pic] (e) [pic]
29) If [pic] is the function given by [pic], at what value of x is the slope of the tangent line to [pic] equal to 2?
(a) -0.135 (b) 0 (c) 0.231 (d) -0.366 (e) 0.693
32) Let f be the function given by [pic]. For what value of x is the slope of the line tangent to the curve at [pic] equal to 1?
(a) 1.099 (b) 0.086 (c) 0 (d) -0.086 (e) -1.099
6) The tangent line to the curve [pic] at the point (2, 8) has an x-intercept at
(a) (-1, 0) (b) (1, 0) (c) (0, -8) (d) (0, 8) (e) (8, 0)
15) The equation of the line normal to [pic] at [pic] is
(a) [pic] (b) [pic] (c) [pic]
(d) [pic] (e) [pic]
1) What is the slope of the line tangent to the curve [pic] when [pic]?
(a) [pic] (b) [pic] (c) -1 (d) 0 (e) [pic]
7) The line normal to the curve [pic] at [pic] has slope
(a) [pic] (b) [pic] (c) 1 (d) [pic] (e) -1
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