Tangent line horizontal

  • #1

Homework Statement



I have a homework that i couldn't do :( can you explain it to me please ?
the problem is :
find all values of x=c so that the tangent line to the graph of f(x) af (c , f(c)) will be horizontal
http://img13.imageshack.us/img13/4222/scan0002izs.jpg [Broken]





The Attempt at a Solution


i know in the end the answer will be x = 2 ... but i wanna how did we get it
 
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Answers and Replies

  • #2
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Consider y = x2 - 4x + 5.

The graph of this equation is a parabola that opens up. By completing the square you can find the vertex and the coordinates of the vertex. The tangent line to this graph is horizontal at the vertex.

The function you have is related to this in that all of its y-values are the square roots of the y-values on the parabola.

Hope this is enough of a hint.
Mark
 

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