Question 988900
{{{m=(f(x+h)-f(h))/h}}} limit as h approaches 0
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{{{m=((1/(x+h))-(1/x))/h}}} Multiply by (x+h)/(x+h)
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{{{m=((1-(x+h)/x))/(h(x+h))}}} Multiply by x/x
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{{{m=(x-(x+h))/(xh(x+h))}}} 
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{{{m=(x-x-h)/(xh(x+h))}}}
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{{{m=-h/(xh(x+h))}}} Cancel out h.
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{{{m=-1/(x(x+h))}}} Where x=3 and h=0
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{{{m=-1/(3(3+0))=-1/9 }}}
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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( 500, 500, -5, 5, -5, 5, 1/x, (-1/9)x+(2/3)) }}}