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Description: f(x)=3/x , find f'(x)find equation of tangent line to y=f(x) at (1,3)

Math

Calculus

f(x)=3/x , find f'(x) find equation of tangent line to y=f(x) at (1,3)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 6YT

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Topic Video

Question

f(x)=3/x , find f'(x)

find equation of tangent line to y=f(x) at (1,3)

Expert Solution

Step 1 Formula Used

Derivate of xⁿ = nx^n-1

$\frac{1}{x} = x^{- 1} {(x^{- 1})}^{'} = - 1 x^{- 1 - 1} = - x^{- 2} {(\frac{1}{x})}^{'} = - \frac{1}{x^{2}}$

and

Equation of line at (a, b) :

(y-b) = m(x-a)

where m is slope of line

slope of line (m) = $\frac{d y}{d x}$

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