number 1 and 2 are giving me some trouble. do i need to use the derivatives to f

Question

number 1 and 2 are giving me some trouble. do i need to use the derivatives to find the max or the min of these problems? and if so how

1. Consider the function f(x-xln(x + 1 . Find the absolute maxmum and absolute minimum on the interval 0.3 2. For each of the following functions, find the critical points, maximum/minimum(s), intervals of increase/decrease, inflection points, intervals of concave up and concave down, and sketch a graph of the function. - 2 (a) f()3 +3a2 +6x (b) /(x)=x2-9 (c) f(x)=n/2-x

Explanation / Answer

1. f(x) = x ln (x+1)

f '(x) = ln(x+1) + x/(x+1)

Critical number, f '(x) =0

ln(x+1) + x/(x+1) =0

x =0

f(0) =0

f(3) = 3 ln(3+1) = 3ln 4 = ln 43= ln 64

Absolute maximum is at x=3 which is ln 64 and absolute minimum is 0 at x=0

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