Posted by Matt on Thursday, April 21, 2011 at 9:23pm.
Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?
So confused

calculus  bobpursley, Thursday, April 21, 2011 at 9:45pm
y=mx+b f'(3)=5 means m=5
y=5x+b but f(3)=2 means
2=5*3+b, or b= 13
tangent line y= 5x13
so the zero is 0=5x13 x=13/5

calculus  Mgraph, Thursday, April 21, 2011 at 9:51pm
That approximation is the intersection of
the tangent and Xaxis.
The equation of the tangent:
y2=5(x3)
If y=0 then x=13/5

calculus  bobpursley, Thursday, April 21, 2011 at 9:53pm
nice work, Mgraph.
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