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I have already obtained the answer by using the quotient rule and so there are stationary points at x = 0 and x = 8. I am fine at doing these types of questions but I don't fully understand the meaning behind the answer. This was also provided in the solution of the answer

Now y approaches infinity as x approaches infinity, and y approaches infinity as x approaches 4^(+). Hence, x = 8 must be a minimum. Similarly, y approaches (-)infinity as x approaches (-)infinity and as x approaches 4^(-). Hence x = 0 is a maximum.

How do you know that x=8 is a maximum and x=0 is a minimum also what does the 4^(+) and 4^(-) mean ? sorry if this is a silly question I just don't get what the final answer says.

David G. Stork
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Cinna
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1 Answers1

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Take the second derivatives to determine whether a function is maximized or minimized at a point.

$4^+$ means approaching the point $4$ from above.

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David G. Stork
  • 29,774
  • if it is $y=\frac{x^2}{x-4}$ it is a hyperbola with one vertical and one slanted asymptote. For some reason we've had several in the past few days – Will Jagy Jan 15 '19 at 02:32
  • Okay thanks for the help I understand it now. – Cinna Jan 16 '19 at 02:07