Question

Find the slope of the tangent line
`m_(tan)` = f'(a) and then find the equation of the tangent line to f at x = a

f(x) =
`(10)/(x)` ; a = 3

Answer 1

9514 1404 393

Answer:

10x +9y = 60

Explanation:

The equation for the tangent line at a point is ...

y -f(a) = f'(a)(x -a)

For the given function,

f(x) = 10/x

The derivative is ...

f'(x) = -10/x^2

Then the equation of the tangent line is ...

y -10/3 = -10/9(x -3) . . . . equation of the tangent line (point-slope form)

Clearing fractions, we have ...

9y -30 = -10(x -3) = -10x +30

10x +9y = 60 . . . . . equation in standard form