# Thread: Differential Calculus - Gradient of the Tangent

1. ## Differential Calculus - Gradient of the Tangent

Hi

Find the gradient of the tangent on the curve $\displaystyle \frac{x}{\sqrt{2x}}$ at the point (4, $\displaystyle \sqrt{2x}$). Express your answer as a rational number.

The textbook's answer is $\displaystyle \frac{\sqrt{2}-2}{2}$ whilst I keep getting $\displaystyle \frac{\sqrt{2}}{8}$. Is the textbook right?

Hello xwrathbringerx
Originally Posted by xwrathbringerx
Hi

Find the gradient of the tangent on the curve $\displaystyle \frac{x}{\sqrt{2x}}$ at the point (4, $\displaystyle \sqrt{2x}$). Express your answer as a rational number.

The textbook's answer is $\displaystyle \frac{\sqrt{2}-2}{2}$ whilst I keep getting $\displaystyle \frac{\sqrt{2}}{8}$. Is the textbook right?
If the equation of the curve is $\displaystyle y=\frac{x}{\sqrt{2x}}$ then you are right - assuming that you mean the point $\displaystyle (4, \sqrt{2})$. But you can't express the answer as a rational number. The best you can do is what you have done: express the answer with a rational denominator.

But are you sure you've read the question properly?