Math 131 Fall 2015
Test 2B
Name:
On my honor, as an Aggie, I have neither given nor received
unauthorized aid on this academic work.
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You may use your calculator for all problems on the test but be sure to read each problem
carefully. Some problems ask you to show some algebraic steps.
Below is the graph of the velocity, v(t) of a particle moving left and right on a line. Moving
right is the positive direction. Assume the local max occurs at t = 0, the local min occurs
at t = 2.5, and that v(t) has x-intercepts at t = −1, 2, 3. Let d(t) be it’s position function
and a(t) be it’s accelartion function.
1.
(2 points) At t = 1/2, d(t) is concave down.
True
2.
(2 points) v(0) = 0.
True
3.
False
(2 points) At t = −1/2 the particle is moving right.
True
4.
False
False
(2 points) d(t) has a horizontal tangent at t = 2.5.
True
False
5.
(6 points) Which of the graphs below is a possible sketch of the derivative of the above
function.
131 Fall 15/Test2AGraph3.png 131 Fall 15/Test2AGraph3.pdf 131 Fall 15/Test2AGraph3.jpg
131 Fall 15/Test2AGraph3.mps 131 Fall 15/Test2AGraph3.jpeg 131 Fall 15/Test2AGraph3.jbig2
131 Fall 15/Test2AGraph3.jb2
6.
(6 points) Let f (t) be the temperature at time t where you live. Let f 0 (1) = −2 and
f 00 (1) = 3. Then this means what about the temperature?
(a) The temperature is increasing at an increasing rate.
(b) The temperature is decreasing at an increasing rate.
(c) The temperature is increasing at a decreasing rate.
(d) The temperature is decreasing at a decreasing rate.
7.
(6 points) Given the table of data, estimate f 0 (2.5).
x
2.3 2.4 2.5 2.6 2.7
f (x) 2 2.1 3
4 4.2
(a) Between 3 and 4
(b) Bewteen 5 and 6
(c) Between 6 and 9
(d) Between 9 and 10
8.
√
(10 points) Find the linearization of f (x) =
3.9. Be sure to show the algebraic steps.
9.
√
x + 2 at x = 2 AND use it to approximate
(10 points) Use derivative rules to prove the derivative of tan(x) is sec2 (x).
10.
(8 points) Find an equation of the tangent line to the curve f (x) = sec(x) at x = π/6.
Give exact answers i.e. leave the square roots as square roots, don’t enter them into your
calculator.
√
Hint: sin(π/6) = 1/2 and cos(π/6) = 3/2.
11.
(10 points) Use definition of the derivative to find the derivative of f (x) =
x
1−x
12.
(12 points) Find f 0 (x) if f (x) = (esin(x) + sin(ex ))(loga (x3 )) Do Not Simplify
13.
(12 points) Find f 0 (x) if f (x) = sin
14.
p
(12 points) Find f 0 (x) if f (x) = cos( sin(tan(πx))) Do Not Simplify
(x+2)3 (x−2)2
Do Not Simplify
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