1. If f(x)=(e2x+1)
8,then f0(1) =
1) 8 ¡e2+1
¢72) 16 ¡e2+1
¢73) 8e2¡e2+1
¢74) 16e2¡e2+1
¢7
2. Which of the following functions has a removable discontinuity at
x=0?
1) xsin µ1
x¶2) ln(x)3)
√x−14)
x−1
x2−1
3. The following picture shows the graphs of f,f0, and f00. Identify
each curve.
1 2 3 4 x
-4
-2
2
4
ya:regular , b:dashed , c:thick
1)
f=a
f0=b
f00 =c
2)
f=c
f0=b
f00 =a
3)
f=a
f0=c
f00 =b
4)
f=b
f0=c
f00 =a
4. Consider the function f(x)=x3−6xon the interval [−2,2].
Which of the following statements is true?
1) The absolute maximum value of fis 4.
2) The absolute maximum value of fis 4√2.
3) The absolute maximum value of fis 5.
4) There is no absolute maximum value of fon the interval.
5. Suppose z=x3y2where both xand yare changing with time.
At a certain instant when x= 1 and y=2,xis decreasing at the rate
of 2 units/sec and yis increasing at the rate of 3 units/sec. How fast
is zchanging at this instant and is it increasing or decreasing?
1) zis increasing at the rate of 24 units/sec.
2) zis decreasing at the rate of 24 units/sec.
3) zis increasing at the rate of 12 units/sec.
4) zis decreasing at the rate of 12 units/sec.
A1
