Homework SourseFind the equation of the tangent line to the curve y x1x at
Find the equation of the tangent line to the curve
y = x-(1/x) at x = 3/2.
Find the value of x-(1/x) and its derivative at x = 3/2.
f(3/2) =
f \'(3/2) =
y = x-(1/x) at x = 3/2.
Find the value of x-(1/x) and its derivative at x = 3/2.
f(3/2) =
f \'(3/2) =
Solution
y = x-(1/x)
Slope = dy/dx = 1 - 1/x^2
Therefore
at x = 3/2
dy/dx = 1 - 4/9
= 5/9
f(3/2) = (3/2) - (2/3)
Therefore
Equation
(y - 5/6) = (5/9)(x - 3/2)
Therefore
y = 5x/9
