Question

Find the equation of the tangent line of the given function at the point with the indicated x-coordinate.
f(x) = x + (1/x); x = 4

y= ? (find the equation)

Answer 1

when x=4
y=?

Answer 2

\[f \prime(x)=1-\frac{ 1 }{ x^2 }\]
at x=4
\[f \prime \left( x \right)=1-\frac{ 1 }{ 16 }=\frac{ 15 }{ 16 }\]
eq. of tangent is
\[y-y1=f \prime \left( 4 \right)\left( x-4 \right)\]
when x=4,
\[y=4+\frac{ 1 }{ 4 }=\frac{ 17 }{ 4 }\]
\[y1=\frac{ 17 }{ 4 }\]