Math 1507

Nov  6, 1997
Tom Morley
Name: ____________________________

Don't Panic

Open Book and Notes. You have 40 minutes. Carefully explain your proceedures and answers

Problem 1 (6 points)

Show below is a plot of f(x) identify all critical point and all inflection points
.

Calculations

junk = (x-2.5)x(x-2)(x-1)^4

(x - ) (x - 2) (((x - 1))^2) x

(x - 4 (x - 2) (((x - 1))^2) x

junk1 = Integrate[junk,x]

Plot[junk1,{x,-.6,4}]

Problem  2 (10 Points)

Shown is f'(x):

Assuming that f(0) = 0 , sketch a picture of f(x)

Calculations

junk = x^2 (x-1)(x+1)(x+3)^2

Plot[junk,{x,-2,2}]

Plot[Evaluate[D[junk,x]],{x,-2,2}]

junk1 = Integrate[junk,x]

Plot[junk1,{x,-2,2}]

Problem 3 (9 Points)

The The derivatives of the follwing 4 functions on the left are in a different order on the right. Match up the functions and the derivatives.

Calculations

f1[x_] := (x-1) Sin[x]

p1 = {Plot[f1[x],{x,-2,3}],
      Plot[f1'[x],{x,-2,3}]}

f2[x_] := (x-2) Cos[x]

p2 = {Plot[f2[x],{x,-2,3}],
      Plot[f2'[x],{x,-2,3}]}

f3[x_] := x^2 Cos[2 x]

p3 = {Plot[f3[x],{x,-2,3}],
      Plot[f3'[x],{x,-2,3}]}

f4[x_] := x^2 Sin[2 x]

p4 = {Plot[f4[x],{x,-2,3}],
      Plot[f4'[x],{x,-2,3}]}

Show[
GraphicsArray[{
    {First[p4],Last[p2]},
    {First[p2],Last[p3]},
    {First[p3],Last[p4]}}]]

Problem 4 (10 Points)

A plane is flying awith a constant speed of 300 km/hr
at a height of 1 km.  The plane flies over a ground radar installation. One half hour later, how fast is the distance
from the plane to the radar installation changing?