a. Graph the function. b. Draw tangent lines to the graph at point whose x -coordinates are –2, 0, and 1. c. Find f ' ( x ) by determining lim x → 0 f ( x + h ) − f ( x ) h . d. d) Find f ' ( − 2 ) , f ' ( 0 , ) and f ' ( 1 ) . These slopes should match those of the lines you drew in part ( b ). f ( x ) = − 2 x 2
a. Graph the function. b. Draw tangent lines to the graph at point whose x -coordinates are –2, 0, and 1. c. Find f ' ( x ) by determining lim x → 0 f ( x + h ) − f ( x ) h . d. d) Find f ' ( − 2 ) , f ' ( 0 , ) and f ' ( 1 ) . These slopes should match those of the lines you drew in part ( b ). f ( x ) = − 2 x 2
Solution Summary: The author illustrates the graph of the function f(x)=-2x-2.
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
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13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
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11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY