[Core 3] Differentiation

Question 9.

For the first part, I tried differentiating it which gave me
4 + x^(-2) then equalling it to 0, but that has no real roots as it gives me x^2 = -(1/4)

Also not sure about the second part.

I think you've differentiated 1/x wrong. rewrite it as x^-1 and see if you get the same answer
Also for the second part consider what happens as x tends to infinity

Holy ****, can't believe I got that wrong. Ended up with (0.5,4) as my minimum point and (-0.5,-4) as my maximum point.

Not sure what you mean though for the second part. Is it that y gets infinitely bigger?

Well as x gets bigger and bigger, then 1/x gets smaller and smaller, therefore as x tends to infinity 1/x tends to zero. So as x gets very large the 1/x component becomes irrelevant, thus y will tend to x meaning there's an oblique asymptote of y=x.

The answer in the text book says x=0 though, is it wrong? Wouldn't be the first time if it was

Well as x gets bigger and bigger, then 1/x gets smaller and smaller, therefore as x tends to infinity 1/x tends to zero. So as x gets very large the 1/x component becomes irrelevant, thus y will tend to x meaning there's an oblique asymptote of y=4x.

x = 0 is the correct and only relevant answer. There is another asymptote at y = 4x which is known as an oblique asymptote, however you're not expected to know what they are for C3/C4 as far as I'm aware.

The answer in the text book says x=0 though, is it wrong? Wouldn't be the first time if it was