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Anthonyn2121
 one year ago
Find the slope of the curve at the given point P, and an equation of the tangent line at P
y=x^23, P(2,1)
Anthonyn2121
 one year ago
Find the slope of the curve at the given point P, and an equation of the tangent line at P y=x^23, P(2,1)

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tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0You will need the first derivative. Go!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\rm y'(x)=2x\) good :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2A tangent line is just a straight line. So it'll have the form: \(\large\rm y=mx+b\) in slopeintercept form and \(\large\rm yy_1=m(xx_1)\) in pointslope form. The process of taking the derivative of the function is what gives us our \(\large\rm m\).

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So at the point P(2,1), our x coordinate is 2. So we want to know the slope of our function (the derivative value), at x=2.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm y'(2)=2(2)=m\]Ok with that part? :o

Anthonyn2121
 one year ago
Best ResponseYou've already chosen the best response.0Yup, that makes sense

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2To get your final answer it would probably make more sense, at least for this problem, to go with pointslope form of a line. \[\large\rm yy_1=m(xx_1)\]Plug in your \(\large\rm m\), plug in your \(\large\rm P\), and bam you're done.
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