The logarithmic function f(x) = -300 + 83 ln x models the number of visitors (in millions) to U.S. museums from 1960 to 2010, where x is the number of years since 1960. Is this function increasing or decreasing?
a)increasing
b)decreasing
logarithm help?
2015-07-08 10:46 pm
回答 (2)
2015-07-08 10:52 pm
f'(x) = 83/x which is always positive
a)increasing
a)increasing
2015-07-08 10:50 pm
We look at the variable part of the function, 83ln(x) (I don't think that this is actually what you call this portion of the function, but the meaning is obvious, so I'll use it). We note that this is a positive multiple of ln(x), meaning that if ln(x) is increasing, then this is increasing. ln(x) IS increasing, so f is also increasing.
Alternatively, the f'(x)=83/x>0 on (0,infinity), which is the domain of the function in the first place (since ln(x) is defined iff x is a real >0), so since the derivative is positive, the function is increasing.
Alternatively, the f'(x)=83/x>0 on (0,infinity), which is the domain of the function in the first place (since ln(x) is defined iff x is a real >0), so since the derivative is positive, the function is increasing.
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