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 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) (Show Source): You can put this solution on YOUR website!
limit as h approaches 0
.
Multiply by (x+h)/(x+h)
.
Multiply by x/x
.

.
Cancel out h.
.
Where x=3 and h=0
.

.
ANSWER (a): m=-1/9
.
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
.
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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