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)

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)

sshayer · Answer

when x=4
y=?

sshayer · Answer

$$f \prime(x)=1-\frac{ 1 }{ x^2 }$$
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,
$$y=4+\frac{ 1 }{ 4 }=\frac{ 17 }{ 4 }$$
$$y1=\frac{ 17 }{ 4 }$$