Let f(x) = 2x^2 - 3x + 1. Find and simplify f(a + h) - f(a)/h (h notequalto 0).
ID: 3144271 • Letter: L
Question
Let f(x) = 2x^2 - 3x + 1. Find and simplify f(a + h) - f(a)/h (h notequalto 0). Answer: ______ The average number of email messages sent and received per corporate user per day in year t between 2011 (t = 1) and 2015 (t - 5) was projected to be f(t) = 3t + 69 (1 lessthanorequalto t lessthanorequalto 5). The average number of spam emails sent and received per corporate user day for the period under consideration was projected to be g(t) = -0.2t + 13.8 (1 lessthanorequalto t lessthanorequalto 5). Find a function h that gives the projected average number of legitimate (non-spam) emails sent and received per corporate user per day in year t. Answer: ______ The president of a major housing construction firm reports that the number of construction jobs (in millions) created is given by N(x) = 1.42x, where x denotes the number of housing starts, Suppose the number of housing starts in the next t months is expected to be x(t) = 7(t + 10)^2/(t + 10)^2 + 2(t + 15)^2 million units. Use composition to determine the number of jobs that will have been created 6 months from now. Do not round your answer until after your final calculation, and be sure to use correct units when stating your answer. Answer: _______Explanation / Answer
f(x) = 2x2 - 3x +1 we are to find and simplify [f(a+h) - f(a) ] / h such that h is not = 0;
f(a) = 2a2 - 3a + 1
f(a+h) = 2(a+h)2 - 3(a+h) + 1 = 2a2 -3a + 1 + 4ah + 2h2 -3h = f(a) + 4ah + 2h2 -3h
Thus, f(a+h) - f(a) = 4ah + 2h2 -3h
and [ f(a+h) - f(a)] / h = 4a + 2h - 3
Thus, [ f(a+h) - f(a)] / h = 4a + 2h -3
we can calcualte the derivative from here too by going for an infinitely small 'h' such that h-> 0 ;
then 4a+2h-3 = 4a-3
2) Total emails = total spams + total legitmate emails (TLE)
3t + 69 = -0.2t + 13.8 + TLE such that 1<= t <=5
TLE = 3t + 69 +0.2t -13.8 = 3.2t + 55.2
Thus, average number of legitmate emails per corporate user per year in the period 2011 to 2016 is given by 3.2t + 55.2 such that 1<= t<=5;
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