PLEASE SHOW ALL WORK AND GIVE CORRECT ANSWER

Anonymous
timer Asked: Jul 10th, 2015

Question Description

I need all the work shown and all the answers to be correct
m251exam3a_130.pdf


Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 1 1. (10 points) Without consulting a graph, determine the critical number(s) of the following function: f ( x)  (3x  7)5 (4 x  5) 2 Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 2 2. (10 points) A certain function, g, has derivative function g ( x)  5(4 x  9)( x  1) 4 . Determine the critical number(s) of g and classify it (them) using the First Derivative Test. (No other method will be accepted.) Also, list the interval(s) on which g is increasing and the interval(s) on which g is decreasing. Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 3 3. (10 points) Without consulting a graph, determine the absolute extreme points of the function f ( x)  x3e3 x on the closed interval  2  x  1 . Bob Brown Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. CCBC Dundalk 4 4. (10 points) Without consulting a graph, determine the inflection point(s), if any, of the function g ( x)  ln 1  x 2 .   Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 5 5. (10 points) Suppose that a function f has critical numbers -3 and 0. Suppose also that the second derivative function of f is f ( x)  4 x 3  2 x  2 . Determine which critical number(s), if any, give a local minimum. 6. (10 points) Sketch a function g with domain    x   that has all of the following characteristics. g (0)  2 g ( x)  0 g ( x)  0 for x < 1 g (1)  0 g ( x)  0 for x > 1 7. (10 points) Let h( x)  (a  bx)(c  dx) . Determine lim h( x) and determine the horizontal x  x2 asymptote of h, if there is one. Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 6 8. (15 points) Centering the Sun at the origin of a coordinate system where both the x-axis and y-axis are scaled in 10,000,000s (ten millions), we find Mercury, on one particular day, at the point (4,5). A very fast moving comet follows the parabolic path y  0.01x 2  2 . Determine the point (rounding coordinates to three decimal places—your coordinates may be in units of 10,000,000) in the path of the comet that is nearest to Mercury, and compute the distance (rounding to the nearest mile) from Mercury to that nearest point in the comet’s path. Note that the comet is moving so fast relative to the Sun and to Mercury that we consider both the Sun and Mercury to be approximately stationary. Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 7 9. (15 points) A farmer plans to fence a rectangular pig sty adjacent to a river. The pig sty must contain 600 square meters of land to provide sufficient living space for the pigs. What dimensions would require the least amount of fencing if no fencing is needed along the river? What is that least amount of fencing? 10. (5 points) Write the differential for f(x) = xcos(x). Bob Brown CCBC Dundalk Math 251 Summer 2015 Calculus 1 Exam 3 130 points possible For full credit, show all work, explain fully, follow directions, and use proper notation. 8 11. (15 points) Determine the first degree Taylor polynomial approximation, T(x), for f ( x)  x = 9, and use this linear approximation to estimate x at 9.3 . 12. (10 points) Give an example of a function g(x) and an element, c, of the domain of g for which g (c)  0 but at which g has neither a relative minimum nor a relative maximum. You must provide the formula for g and sketch its graph and also identify the value of c. Also, answer the question: Under the conditions of this problem, is c a critical number of g? Explain.

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