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Bandarsso

Answered question

2022-02-11

How do you find the equation of the line tangent to the graph of

f (x) = \frac{10}{5 x + 9}

, when x =1/5?

ungabav6k

Beginner2022-02-12Added 8 answers

The equation of the Tangent line has the form y=mx+n
At first we will compute the first derivative of f(x)

f (x) = 10 {(5 x + 9)}^{- 1}

then we get

f^{'} (x) = - 10 {(5 x + 9)}^{- 2} \cdot 5 = - \frac{50}{{(5 x + 9)}^{2}}

by the chain rule.
and

f^{'} (\frac{1}{5}) = - \frac{50}{{(5 \cdot \frac{1}{5} + 9)}^{2}} = - \frac{50}{100} = - \frac{1}{2}

so the slope is given by

m = - \frac{1}{2}

The Point is given by

f (\frac{1}{5}) = \frac{10}{10} = 1

so we have

1 = - \frac{1}{2} \cdot (\frac{1}{5}) + n

n = \frac{11}{10}

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