Given the function , state the equations of all the asymptotes and find the turning points, stating the domain.
Please show complete working out. I don't know how to find out the above.
Given the function , state the equations of all the asymptotes and find the turning points, stating the domain.
Please show complete working out. I don't know how to find out the above.
Your previous method of partial fractions is useful for calculating the derivative of quotients.
Alternatively, use the Quotient Rule.
However, in this case, it's convenient to use a "negative exponent" instead.
Using the Chain Rule
This is zero when the numerator is zero, if we do not have an or factor there.
(all the work calculating the denominator is often a waste of time, but not always).
Since
There is a turning point at that x, provided ,
otherwise, we'd have calculated a turning point at the asymptote, which is not possible.
Then place that x into to find the vertical co-ordinate of the turning point.
Alright, alright, makes sense. I don't really pretend to be good at all this maths stuff.
I'm also not getting the correct corresponding y value when I algebraically substitute the x value of the turning point in f(x). Would anyone be able to supply the rest of the working out to see where I went wrong?