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= 5x-13

so the zero is 0=5x-13 x=13/5

- calculus -
**Mgraph**, Thursday, April 21, 2011 at 9:51pm
That approximation is the intersection of

the tangent and X-axis.

The equation of the tangent:

y-2=5(x-3)

If y=0 then x=13/5

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

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