Question
Asked Sep 23, 2019
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Let f(x) = (x - 12) / (2x + 6)

Find an equation for the tangent line to the graph of f at x = 2

y = ?

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Expert Answer

Step 1

We find f'(x) first using quotient rule

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x-12 f(x)2x+6 f'(x)=(X-12)(2x+6)-(x-12)(2x+6)' (2x+6) f'(x)(1)(2x+6)-(x-12)(2) (2x+6) 2х+6-2х+24 f'(x) (2x+6)2 30 f'(x)= (2x+6)2

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Step 2

Slope= f'(2)

And y=f(2)

So, slope=...

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30 f'(x)= (2x+6)2 x-12 f(x)= 30 2x+6 f'(2)= (2(2)+6) 2-12 f(2) 30 f'(x)= (10)2 2(2)+6 -10 f(2) 10 30 f'(x) 100 f(2) - f'(x) 10

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Tagged in

Math

Calculus

Derivative