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Core 2

A curve with equation y=f(x) such that

\frac{dy}{dy}

= 3x to the power of half - 2x to the power of minus a half and x>0.

a, Find the gradient of the curve at the point where x=2, giving your answers in its simplest form.
I substituted 2 in for x to get 3

\sqrt 2

- 2

\sqrt 2

\sqrt 2

.
But, the mark scheme says that the answer is 2

\sqrt 2

???

Reply 1

Pangol

Have another look at what you get when you substitute x=2 - your version isn't quite right. Don't forget the minus in the second power!

Reply 2

Chelsea12345

Original post by Pangol

Have another look at what you get when you substitute x=2 - your version isn't quite right. Don't forget the minus in the second power!

i keep getting the same answer! what would you say 2 to the power of -1/2 then multiplied by 2 is?

Reply 3

Pangol

2 to the power of -1/2 is one over root 2, so you have 3 root 2 subtract 2 over root 2. You now have to rationalise the denominator of the second term before you can combine them.