First Course in the Theory of Equations
First Course in the Theory of Equations
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In our eReader you can find the full English version of the book. Read First Course in the Theory of Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book First Course in the Theory of Equations
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To quickly assess the difficulty of the text, read a short excerpt:
Any root a of f'(x)=0 is the abscissa of a bend point of the graph of y =f(x) or of a point with a horizontal inflexion tangent according as the value of m for which relations (13) hold is even or odd.
For example, if /(x) x 4, then = and TO = 4, so that (0, 0) is a bend point of the {/-shaped graph of y = x 4 . If /(x)=x 3, then a = and TO = 3, so that (0, 0) is a point with a horizontal inflexion tangent (OX in Fig. 15) of the graph of y=x 3 .
EXERCISES 1. If /(x)=3x 5 -r-5x s +4, the only re...al root of /'(x)=0 is x = 0. Show that (0, 4) is an inflexion point, and thus that there is no bend point and hence that /(x) = has a single real root.
2. Prove that x 3 3x 2 +3z+c = has an inflexion point, but no bend point.
3. Show that x 5 10x 3 20x 2 15x+c = has two bend points and no horizontal inflexion tangents.
4. Prove that 3x 5 40x 3 +240x+c = has no bend point, but has. Two horizontal inflexion tangents.
5. Prove that any function x 3 3ax z + ... Of the third degree can be written in the form /(x) = (x a) 3 +ox+6.
What to read after First Course in the Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Leonard E Leonard Eugene Dickson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Any root a of f'(x)=0 is the abscissa of a bend point of the graph of y =f(x) or of a point with a horizontal inflexion tangent according as the value of m for which relations (13) hold is even or odd.
For example, if /(x) x 4, then = and TO = 4, so that (0, 0) is a bend point of the {/-shaped graph of y = x 4 . If /(x)=x 3, then a = and TO = 3, so that (0, 0) is a point with a horizontal inflexion tangent (OX in Fig. 15) of the graph of y=x 3 .
EXERCISES 1. If /(x)=3x 5 -r-5x s +4, the only re...al root of /'(x)=0 is x = 0. Show that (0, 4) is an inflexion point, and thus that there is no bend point and hence that /(x) = has a single real root.
2. Prove that x 3 3x 2 +3z+c = has an inflexion point, but no bend point.
3. Show that x 5 10x 3 20x 2 15x+c = has two bend points and no horizontal inflexion tangents.
4. Prove that 3x 5 40x 3 +240x+c = has no bend point, but has. Two horizontal inflexion tangents.
5. Prove that any function x 3 3ax z + ... Of the third degree can be written in the form /(x) = (x a) 3 +ox+6.
What to read after First Course in the Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Leonard E Leonard Eugene Dickson to read onlineMoreLess
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