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

Algebra ->  Equations -> 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      Log On


   

Question 988900: 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.
Thank you
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
m=%28f%28x%2Bh%29-f%28h%29%29%2Fh limit as h approaches 0
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m=%28%281%2F%28x%2Bh%29%29-%281%2Fx%29%29%2Fh Multiply by (x+h)/(x+h)
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m=%28%281-%28x%2Bh%29%2Fx%29%29%2F%28h%28x%2Bh%29%29 Multiply by x/x
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m=%28x-%28x%2Bh%29%29%2F%28xh%28x%2Bh%29%29
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m=%28x-x-h%29%2F%28xh%28x%2Bh%29%29
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m=-h%2F%28xh%28x%2Bh%29%29 Cancel out h.
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m=-1%2F%28x%28x%2Bh%29%29 Where x=3 and h=0
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m=-1%2F%283%283%2B0%29%29=-1%2F9+
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ANSWER (a): m=-1/9
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Slope is (-1/9), tangent point is (3,1/3)
Equation in slope intercept form:
y=mx+b
y=(-1/9)x+b Use tangent point to find b.
(1/3)=(-1/9)3+b
1/3=-1/3+b
2/3=b Put b value in for final equation
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ANSWER (b). Equation for tangent line is y=(-1/9)x+2/3
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Now we know y intercept is (0,2/3), let y=0:
0=(-1/9)x+2/3
-2/3=(-1/9)x
6=x
And the x intercept is (6,0)
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ANSWER (c): Intercepts: (6,0).(0,2/3)
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Original function in red, tangent line in green.
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+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+1%2Fx%2C+%28-1%2F9%29x%2B%282%2F3%29%29+