Last Minute Q

[sxcalexc]

In regards to last question on the 2007 exam 1. I understand how to use the distance between points formula, but not how they worked it out from the square root. For the first solution what is d(l^2)/dx ? How can you differentiate like that? For their second solution, how did they arrive at the minimum so easily (without chain rule differentiation). Thanks guys

[/0]

Not so sure about the first one, but the second one uses the fact that the turning point of a parabola is halfway between its x-intercepts.



Since the coefficient is positive, the turning point will give the minimum value of . By taking the average of x-intercepts and , the x-coordinate of this turning point is found.

[sxcalexc]

Not so sure about the first one, but the second one uses the fact that the turning point of a parabola is halfway between its x-intercepts.



Since the coefficient is positive, the turning point will give the minimum value of . By taking the average of x-intercepts and , the x-coordinate of this turning point is found.

Ahh nice one, cheers /0!

[shinny]

For the first one, since you're trying to find the maximum of , it's easier to just square it and then differentiate to find the maximum of as the maximum's of both functions are equal  for their x-values, as squaring the largest number in a function will lead to it being the largest number in the next as well (as long as this number is greater than 1 of course). And yeh, only reason you do this is just to make it easier to differentiate, since having a polynomial/no chain is clearly better :]

[sxcalexc]

For the first one, since you're trying to find the maximum of , it's easier to just square it and then differentiate to find the maximum of as the maximum's of both functions are equal  for their x-values, as squaring the largest number in a function will lead to it being the largest number in the next as well (as long as this number is greater than 1 of course). And yeh, only reason you do this is just to make it easier to differentiate, since having a polynomial/no chain is clearly better :]

Ah.. I think I get it.. , so the x value remains the same but not the y?

[vce01]

ughh i did not get that question at all, can someone explain it?

[shinny]

Yep pretty much, but you're only interested in the x value to know when is at a maximum anyway so it's all good.

[onlyfknhuman]

lol that is so confusing i rather do it the old way.