Question

Its from Calculus grade 12 my question is
Determine the slope of the tangent at x=2 for the function y=8/x.

Answer 1

The slope of the tangent line for any function, f(x), at x, it is the derivative of the function with the x you are looking for plugged in. So take the derivative of your function, then plug in your x.

Answer 2

Take the derivative of the function y = 8/x by applying the quotient rule:
\[\frac{ f(x) }{ g(x) } = \frac{ f'(x)g(x)-f(x)g'(x) }{ ^{g(x)2} }\]
then substitute x for 2 and solve for y.

Answer 3

Another trick is to rewrite the equation with the exponents on top. I would rewrite yours as:
\[y=8 \cdot x^{-1}\]
And then derived as normal.