#21 Families of functions Draw the graphs of the family of functions f(x) = a/2

Question

   #21

Families of functions Draw the graphs of the family of functions f(x) = a/2 (e^r/e + e^-r/e) for a = 0.5. I, 1.5, and 2. How does n larger value of a affect the graph? The Definition of e Illustrate (he definition of the number e by graphing the curve y = (1 + 1/x)^x and the line y = e on the same screen, using the viewing rectangle [0. 40] by [0. 4]. Local Extrema Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer rounded to two decimal places. g(x) = x^x, x > 0 g(x) = e^x + e^-2x

Explanation / Answer

g(x) = x^x

g'(x) = x^x( lnx +1)

g'(x) =0 ; x^x( lnx +1) =0

lnx = -1 ; x = 1/e

find 2nd derivative : g"(x) = x^x(lnx +1)^2 + x^(x-1

g'(1/e) >0

So, x = 1/e is a minimum point

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