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find the slope of the tangent line [tex]m_{tan}[/tex] = f'(a) and then find the equation of the tangent line to f at x = a

f(x) = [tex]\frac{10}{x}[/tex] ; a = 3

Sagot :

Sqdancefanidn

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Answer:

 10x +9y = 60

Step-by-step 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

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