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Calculus/Calculus Derivatives

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Expert: - 8/30/2008


Question
If f(2) = 3 and the derivate of f(2) = 5, find an equation of
a) the tangent line, and
b) the normal line to the graph of f(x) at the point where x=2.

Answer
We know a point (2,3)=(x0,y0) and the slope is 5=m, so use the point-slope form of the equation of a line which is y-y0 = m(x-x0).

Since x0=2, this is the line that uses x=2, and the equation of a normal is the equation of the perpendicular.  To find a perpendicular line, the equation of it is (y-y0)=(-1/m)(x-x0).
Again, x0,y0, and m are known, so put them into this equation.

These equations can be simplified a little bit if necessary.

Calculus

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