Question

Find the slope m of the tangent to the curve
y = 5/sqrt(x) at the point where x = a > 0.

Answer 1

The slope of the line tangent to \(\Large\rm y(x)\) at x=a will be given by \(\Large\rm y'(a)\).

Answer 2

Hmm, so we need to take a derivative.
Understand how to do that?

Answer 3

the derivative is \[5\div x ^{2}\]

Answer 4

Hmm that looks a little bit off :O

Answer 5

\[\Large\rm y=5x^{-1}\]We should be getting a negative showing up somewhere when we differentiate, yes?

Answer 6

\[-5\div 2a ^{5/2}\]

Answer 7

Hmm that looks kinda strange D:

Answer 8

Was this the function we started out with?\[\Large\rm y=\frac{5}{x}\]

Answer 9

yes

Answer 10

oh no im sorry it was 5\[5\div \sqrt{x}\]

Answer 11

\[\Large\rm y=\frac{5}{\sqrt{x}}\]Let's write our x with a rational exponent:\[\Large\rm y=\frac{5}{x^{1/2}}\]And bring it up to the numerator:\[\Large\rm y=5x^{-1/2}\]Now we can easily apply our power rule to find the derivative.

Answer 12

\[\Large\rm y'=-\frac{1}{2}\cdot 5x^{(-\frac{1}{2}-1)}\]Power rule, yes? :)

Answer 13

y'= \[-1\div2 \times5x ^-3\div2\]

Answer 14

Mmm good good good :)

Answer 15

So your solution was very close. Looks like you got a -5/2 the first time by mistake instead of -3/2 for the exponent.

Answer 16

thank you