Schaum's Outline of Beginning Calculus by Elliott Mendelson

Author:Elliott Mendelson
Language: eng
Format: epub, pdf
Publisher: McGraw-Hill Education
Published: 2008-04-10T04:00:00+00:00

Since dx = Δx, the definition of the differential df can be rewritten as

Assuming that dx = Δx ≠ 0, we may divide both sides by dx, obtaining the result

If we let y = f(x), this may explain the traditional notation dy/dx for the derivative.

21.3 NEWTON’S METHOD

Let us assume that we are trying to find a solution of the equation

and let us also assume that we know that x0 is close to a solution. If we draw the tangent line to the graph of f at the point with abscissa x0, then will usually intersect the x-axis at a point whose abscissa x1 is closer to the solution of (21.4) than x0 (see Fig. 21-2).

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