SOLUTION: find the average rate of change of the function f(x)=sqrt(1-2x^2) between x=-a and x=-a+h.
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Question 661150: find the average rate of change of the function f(x)=sqrt(1-2x^2) between x=-a and x=-a+h.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The average rate of change of a function between two points is given by the formula for the slope of the secant line through the two points.
\ -\ f(x_1)}{x_2\ -\ x_1} )
where \right))
and \right))
are the coordinates of the given points.
Where the two abscissas differ only by a constant, 
in your problem, the denominator simplifies to just that constant.
\ -\ f(-a)}{h} )
All you need to do is to evaluate the function at 
and 
, simplify the numerator, divide out the because every term in the simplified numerator (given correct algebra) will contain at least one factor of .
In the case of your problem, simplifying the numerator is somewhat more than a trivial exercise because you will have the difference of two expressions containing radicals and you will not be able to reduce the two radicands to be equal expressions. The trick is to rationalize the numerator. The process is the same as rationalizing a denominator, except that you will choose the conjugate of the numerator so that when you multiply you get the difference of two squares effectively eliminating the numerator radicals. You will still have radical expressions in the denominator, but you will be able to eliminate the factor of in the denominator because you have taken all of the factors of out of the radicals in the numerator.
John
My calculator said it, I believe it, that settles it
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