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\centerline{Math131-503 \hfill Quiz \# 2B \hfill Spring 1992}
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Name \hskip 2in Id. \# 
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Show your work.

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1. (7 pts) Use limits to compute $f'(4)$ when $ f(x) = \sqrt{2x-1} $.

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2. (4 pts) Let 
$$
f(x) = \left\{ 
{ { x+1 \hbox{ for } x \le 1 } \atop { 2x \hbox{.\hskip 12pt for } x > 1 } }
\right.
$$
Is $f$ continuous at $ x = 1 $?
Is $f$ differentiable at $ x = 1 $? Give reasons.

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3. (6 pts) Compute the following:
$$
\hbox{\rm a)} f''(x) \hbox{ if } f(x) = x^3 - { 1 \over x }
\hbox{\hskip .5in \rm b)} 
\left. { d \over dz } ( z^4 - 4 ) ^3 \right|_{z=1}
$$

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4. (3 pts) Suppose the weight, in grams, of cancerous tumor at 
time $t$ is $ W(t) = .1 t^4 $, where $t$ is measured in weeks.
What is the instantaneous rate of growth  of the tumor
(in grams per week) when $ t = 2 $ ?

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