Question

eqn of tangent line to graph of 4/√x at (1,4)

Answer 1

Hi,

First: write the equation of a line in point slope form using the point (1,4)

y-4=m(x-1).....then find the first derivative of the function provided, which represents the slope of the line tangent to the graph....substitute in the value for x, (which is 1)....and simplify. The result is the numerical value for m in the above equation.
I hope this helps!

Answer 2

\[y=4/\sqrt{x}\]
\[y=4/x ^{1/2}\]
\[y=4x^{-1/2}\]
\[m=y'=-2x ^{-3/2}\]
\[m=-2/x ^{3/2}\]
Therefore at the point (1,4), m=-2
in point slope form..
\[y-4=-2(x-1)\]
\[y-4=-2x+2\]
\[y=-2x+6\]
I hope this helps!