Chapter 4: Problem 2
\(f(x)=\sqrt{x^{2}+9}, \quad a=-4\)
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Moving Shadow A man 6 ft tall walks at the rate of 5 \(\mathrm{ft} / \mathrm{sec}\) toward a streetlight that is 16 \(\mathrm{ft}\) above the ground. At what rate is the length of his shadow changing when he is 10 \(\mathrm{ft}\) from the base of the light?
Multiple Choice Which of the following conditions would enable you to conclude that the graph of \(f\) has a point of inflection at \(x=c ?\) (A) There is a local maximum of \(f^{\prime}\) at \(x=c\) . (B) \(f^{\prime \prime}(c)=0 .\) (C) \(f^{\prime \prime}(c)\) does not exist. (D) The sign of \(f^{\prime}\) changes at \(x=c\) . (E) \(f\) is a cubic polynomial and \(c=0\)
Multiple Choice A continuous function \(f\) has domain \([1,25]\) and range \([3,30] .\) If \(f^{\prime}(x)<0\) for all \(x\) between 1 and \(25,\) what is $f(25) ? (a) 1 (b) 3 (c) 25 (d) 30 (e) impossible to determine from the information given
Multiple Choice If the volume of a cube is increasing at 24 \(\mathrm{in}^{3} / \mathrm{min}\) and the surface area of the cube is increasing at 12 \(\mathrm{in}^{2} / \mathrm{min}\) , what is the length of each edge of the cube? \(\mathrm{}\) \(\begin{array}{lll}{\text { (A) } 2 \text { in. }} & {\text { (B) } 2 \sqrt{2} \text { in. (C) } \sqrt[3]{12} \text { in. (D) } 4 \text { in. }}\end{array}\)
Tolerance The height and radius of a right circular cylinder are equal, so the cylinder's volume is \(V=\pi h^{3} .\) The volume is to be calculated with an error of no more than 1\(\%\) of the true value. Find approximately the greatest error that can be tolerated in the measurement of \(h,\) expressed as a percentage of \(h .\)
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