`f(x) = (x + 4)/(2x - 5), (9,1)` Find and evaluate the derivative of the function at the given point. Use a graphing utility to verify your result.

Textbook Question

Chapter 2, 2.4 - Problem 70 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the equation of the tangent line at (9,1), using the formula:

f(x) - f(9) = f'(9)(x - 1)

Notice that f(9) = 1.

You need to evaluate f'(x), using the quotient rule, such that:

`f'(x) =((x+4)'(2x-5) - (x+4)(2x-5)')/((2x-5)^2)`

`f'(x) = (2x-5 - 2x - 8)/((2x-5)^2)`

`f'(x) = -13/((2x-5)^2)`

You need to evaluate the derivative at x = 9:

`f'(9) = -13/((18-5)^2) =>< f'(9) = -1/13`

Replacing the values into equation yields:

`f(x) - 1= -(1/13)(x - 9)`

Hence, evaluating the equation of the tangent line at the given curve, yields `f(x) = 1 - (1/13)(x - 9).`

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