SOLUTION: Find the following, rounded to two decimal places. (Enter your answers using interval notation.) Y=X4^(x) (a) the intervals on which the function is increasing or decreasing?

Algebra ->  Equations -> SOLUTION: Find the following, rounded to two decimal places. (Enter your answers using interval notation.) Y=X4^(x) (a) the intervals on which the function is increasing or decreasing?      Log On


   

Question 1040468: Find the following, rounded to two decimal places. (Enter your answers using interval notation.)
Y=X4^(x)
(a) the intervals on which the function is increasing or decreasing?
(b) the range of the function?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%2A4%5Ex
Find the derivative,
dy%2Fdx=4%5Ex%28x%2Aln%284%29%29%2B4%5Ex
dy%2Fdx=4%5Ex%28x%2Aln%284%29%2B1%29
So the sign of the derivative is controlled by,
x%2Aln%284%29%2B1
So find when,
x%2Aln%284%29%2B1=0
x%2Aln%284%29=-1
x=-1%2Fln%284%29
The function is decreasing when x%3C-1%2Fln%284%29
The function is increasing when x%3E-1%2Fln%284%29
and it has a minimum when x=-1%2Fln%284%29
When x=-1%2Fln%284%29
y=-1%2F%28e%2Aln%284%29%29
So the range is
[-1%2Fln%284%29,infinity)
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