Question
The functions and are equal at and at . Between and at , for what value of are their graphs furthest apart?
(a)
(b)
(c)
(d)
(e)
Hints
Solutions
Solution
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Within the domain , lower power functions dominate higher power functions. Therefore we will take the derivative of and solve for the local maximum:
To prove that this is a local maximum and not a local minimum we will take the second derivative:
Substituting in for :
When the second derivative is negative and the first derivative is equal to zero we have found a local maximum.
The difference in the values between and is greatest when
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