Calculus I · Unit 2B · answer key

Unit 2B Practice Exam A Answer Key

Finish an honest attempt first, then compare one numbered response at a time and identify the first decision that changed your work.

Answer 1

Problem 1

$v=3t^2-12t+5$ , $a=6t-12$ ; solve $v=0$ and compare signs of $v$ and $a$ .

Answer 2

Problem 2

$\sqrt{25.4}\approx5+0.4/10=5.04$ ; concavity of $\sqrt{x}$ makes the tangent estimate slightly high.

Answer 3

Problem 3

$|dV|\approx28.8\pi$ cm $^3$ ; relative error approximately $1.25\%$ .

Answer 4

Problem 4

Starting $x_0=1.5$ or $2$ gives a root approximately $1.3788$ after continued iteration.

Answer 5

Problem 5

When the bottom is $6$ , height is $8$ ; $dy/dt=-3/4$ ft/s.

Answer 6

Problem 6

$\theta'=0.024$ rad/min.

Answer 7

Problem 7

Average slope $-1/4$ ; solve $-1/c^2=-1/4$ , giving $c=2$ .

Answer 8

Problem 8

$f'=3x(x-2)$ , $f"=6x-6$ ; use sign charts.

Answer 9

Problem 9

Maximum occurs at $x=4/\sqrt3$ ; area $256/(3\sqrt3)$ .

Answer 10

Problem 10

$A'(q)=-1500/q^2+0.01$ ; minimum at $q=100\sqrt{15}$ . Also $A'(100)=-0.14$ .

Answer 11

Problem 11

$2$ .

Answer 12

Problem 12

$4$ .

Answer 13

Problem 13

Peak at $t=2.5$ , concentration $75/e$ , increasing for $0<t<2.5$ .

Answer 14

Problem 14

By the MVT, $|f(5)-f(1)|\le3(4)=12$ .

After the explanation

Use the section idea

Reading lens

Use reference and answer-key pages to diagnose and repair work after an honest attempt, then return to the exact lesson behind the error.

Mental model

A key is most useful when it identifies the first decision that diverged, not merely the final expression.

Decision

Compare one numbered response at a time, annotate the correction, and retry without the key open.

Common trap

Copying a finished solution without locating the modeling, theorem, or algebra decision that needs practice.

Check yourself

Can you reproduce the reasoning independently and explain the units and assumptions in your own words?

Source & rights

Original instruction with traceable references.

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