1. The problem statement, all variables and given/known data
Within the interval ( 22.27, 40.55 ), for what value of x does f(x) take on a minimum if
f(x)=4.7sin(0.1x)−6.1cos(0.1x)
Later the question asks for the maximum as well.
2. The attempt at a solution
I know to find the critical values to take the first derivative and set it equal to zero, then solve for x. When I do that I get the equation...
0=.47cos(.1x)+.61sin(.1x)
When I solve this guy, by manipulating the equation to get tan(.1x)=.47/.61, I get only one value, x=6.56487, which is the minimum value. But I also need a maximum value. I've tried both end points within the interval and they were wrong. Is there something I'm missing here?
Any help would be appreciated.
