SOLUTION: Consider the function f(x) = 1/x I cannot use derivatives, my teacher requires using limits or other methods to solve. (a). Find the slope of the L tangent to the graph of (3

Question 988918: Consider the function f(x) = 1/x
I cannot use derivatives, my teacher requires using limits or other methods to solve.
(a). Find the slope of the L tangent to the graph of (3,f(3))
(b). Find an equation of the line L
(c). Find the x-intercept and y-intercept of L
Please explain how these are figured out. Very confused.
Also, what exactly is 3,f(3) are these just arb pts?
Thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The point (3,f(3)) is the same as (3,1/3) since f(3) = 1/3

Plug x = 3 into f(x) = 1/x to get f(3) = 1/3

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Part a)

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Let's simplify the difference quotient

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Now apply the limit.

As h approaches 0, will approach

So the derivative function is

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Plug x = 3 into the derivative function to get

Therefore, the slope of line L is

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Part b)

The slope of line L is (found earlier). The tangent line L goes through (3,1/3) so x = 3 and y = 1/3.

Plug in , and into . Then solve for b.

The equation of the tangent line L is

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Part c)

The y-intercept is 2/3 or the point (0,2/3). This was found in part b) above.

The x-intercept is found by plugging in y = 0 and solving for x

The x-intercept is 6, which is the same as the point (6,0)

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Graph

is in green

is in blue (tangent line at (3,1/3))

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If you need more help, or if you have any questions about the problem, feel free to email me at
jim_thompson5910@hotmail.com
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