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Let f(x) = 2 + 2x2 - x2 Find the horizontal and vertical asymptotes of the graph

ID: 3001365 • Letter: L

Question

Let f(x) = 2 + 2x2 - x2 Find the horizontal and vertical asymptotes of the graph of f(x). Determine intervals on which f is increasing and intervals on which f is decreasing. Also find local maximum and local minimum values of f. Determine intervals on which f is concave up and intervals on which f is concave down. Also find points of inflection. Sketch the graph of f.

Explanation / Answer

no vertical asmyptote no horizontal asymptote 4x - 4x*X*x > 0 x(x-1)(x+1) < 0 x E (-infinity , -1) U (0 , 1) incresing decreasing (-1 , 0) U (1 , infinity) 4 - 12x*x > 0 x*x < 1/3 x E (-1/sqrt[3] , 1/sqrt[3]) concave up -inifnity , -1/sqrtp[3] ) U (1/sqrt[3] , inifnity) concave down 1!1

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