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Question
I have a question that i cant seem to figure out...
Let f(x)=ax+ b/x where a and b are constants.
a) find in terms of a and b, the intervals on which f is increasing
b) find the coordinates of all local maximum and minimum points
c)On what interval(s) is the graph concave up?
d)Find any inflection points. Explain briefly.
I dont understand how to do this without actually having the numbers and the coordinates. I need help! and fast!
Note that the funciton f(x) can be looked at as a*x^1 + b*x^-1. The derivative of x^n is n*x^(n-1). Note that if the function has a negative exponent, the derivative is never goes to 0.
a) When the first derivative is positive, the function is increasing.
b) When the first derivative is zero, that will give you the x values at the maximum / minimum.
c) Intervals where the second derivative is negative are where the function is concave up.
d) Inflection points are where the second derivative is zero.
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