What is the equation of the tangent line of f(x)=x2x−4 at x=5?

Explanation:First, find the value of f(x) at x=5.f(5)=(5)25−4=25Now, let's find the derivative of f(x) at x=5.ddx(x2x−4)=(2x)(x−4)−x2(x−4)2=f′(x)f′(5)=(10)(1)−25(1)2=−15With all this information, we can set up a tangent line equation for x=5. Here is the answer.y-25=-15(x-5)

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High School
Calculus and Analysis
Calculus 1
Derivatives

Leroy Davidson

Answered question

2022-03-23

What is the equation of the tangent line of

f (x) = \frac{x^{2}}{x - 4}

at x=5?

Answer & Explanation

Nunnaxf18

Beginner2022-03-24Added 18 answers

Explanation:
First, find the value of f(x) at x=5.

f (5) = \frac{{(5)}^{2}}{5 - 4} = 25

Now, let's find the derivative of f(x) at x=5.

\frac{d}{d x} (\frac{x^{2}}{x - 4}) = \frac{(2 x) (x - 4) - x^{2}}{{(x - 4)}^{2}} = f^{'} (x)

f^{'} (5) = \frac{(10) (1) - 25}{{(1)}^{2}} = - 15

With all this information, we can set up a tangent line equation for x=5. Here is the answer.
y-25=-15(x-5)

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