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Cylindrical Container - Calculus - Exam, Exams of Calculus

This is the Exam of Calculus which includes Find, Differentiable, Function, Limit Definition, Derivative, Limits, Evaluate, Calculus, Respect, Elliptic Track etc. Key important points are: Cylindrical Container, Coordinates, Local Extrema, Classify, Local Maximum, Local Minimum, Global Extrema, Inflection Points, Previous, Domain

Typology: Exams

2012/2013

Uploaded on 03/06/2013

nishaa
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MATH 105 Final Exam Review II
1. Consider the function f(x)=x6
−2x3on the interval [−2,2].
(a) Find the x- and y-coordinates of any and all local extrema and classify each as a local maximum
or local minimum.
(b) Find the x- and y-coordinates of any and all global extrema and classify each as a global maximum
or global minimum.
(c) Find the x-coordinate(s) of any and all inflection points.
2. How would your answers to the previous question have changed if the domain of fwere all reals?
pf3
pf4

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MATH 105 Final Exam Review II

  1. Consider the function f(x) = x^6 − 2 x^3 on the interval [− 2 , 2].

(a) Find the x- and y-coordinates of any and all local extrema and classify each as a local maximum or local minimum.

(b) Find the x- and y-coordinates of any and all global extrema and classify each as a global maximum or global minimum.

(c) Find the x-coordinate(s) of any and all inflection points.

  1. How would your answers to the previous question have changed if the domain of f were all reals?
  1. Your company is mass-producing a cylindrical container. The flat portion (top and bottom) costs 3 cents per square inch and the curved (lateral) portion costs 5 cents per square inch. If your budget is $9.00 per container, what dimensions will give the largest volume? area of circle = πr^2 lateral area of cylinder = 2πrh volume of cylinder πr^2 h
  2. Use Newton’s Method to find a root of f(x) = x^3 − x + 1 correct to three decimal places.
  3. Find the Taylor polynomial of order three for f(x) = 3

x based at x = 8.

  1. The rate of change of a room’s temperature is r(t) = t^2 − 9 degrees per hour on the interval [0, 4] hours. At t = 0, the temperature is 70 degrees. (Remember that r is the derivative of the temperature function.)

(a) When on this interval is the temperature rising? falling?

(b) What is the maximum temperature on this interval and when does it occur?

(c) What is the minimum temperature on this interval and when does it occur?

(d) What is the average rate of change of the temperature on this interval?

  1. An object is launched vertically into the air from ground level with an initial velocity of 160 feet per second. Gravity causes a downward acceleration of 32 ft/sec/sec. What is its velocity when it first reaches a height of 256 feet? When it next reaches this same height?