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# discriminant problem watch

1. does the descriminant of the first derivative represent anything and if so could someone tell me what the hell it is. please.
does the descriminant of the first derivative represent anything and if so could someone tell me what the hell it is. please.
Umm, what do you mean by "descriminant of the first derivative"? If you mean discriminant, that is b^2 - 4ac in the quadratic formula (underneath the square root).
3. A cubic equation of the form y = ax³/3 + bx²/2 + cx + d (for arbritrary constants a,b,c,d) has derivative dy/dx = ax² + bx + c. A cubic may have no turning points, one stationary point (inflexion) or two stationary points (maximum and minimum). Since turning points are found by the equation dy/dx = 0 we have ax² + bx + c = 0. The discriminant of this equation determines the number of real solutions and hence the nature of the turning points:

b² - 4ac < 0 => No real solution to dy/dx = 0 hence no turning point

b² - 4ac = 0 => One repeated root to dy/dx = 0 hence a point of inflexion

b² - 4ac > 0 => Two real solutions to dy/dx = 0 so two st. points - one max and one min

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Updated: August 15, 2004
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