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coordinate systems - Abscissa, Ordinate, and Applicate -- Origins . . . The technical use of ‘abscissa’ is observed in the eighteenth century by C Wolf and others In the more general sense of a ‘distance’ it was used earlier by B Cavalieri in his Indivisibles, by Stefano degli Angeli (1623-1697), a professor of mathematics in Rome, and by others ”
Word choice for describing a variation with the abscissa (x) In mathematics, the abscissa (plural abscissae or abscissæ or abscissas) and the ordinate are respectively the first and second coordinates of a point in a coordinate system: Abscissa x-axis (horizontal) coordinate; ordinate y-axis (vertical) coordinate Usually these are the horizontal and vertical coordinates of a point in a two-dimensional
calculus - Find the first coordinate of the intersection point of two . . . Find the abscissa of the intersection point of the two tangent lines of $f (x)$ at $x=-4$ and at $x=2$ I know I'm meant to find the two gradients of the two lines and use simultaneous equations to substitute the values, but I'm not sure how
calculus - Prove if $f (x)=ax^3+bx^2+cx+d$ has two critical numbers . . . The question concerning the relation between the critical points (when they are present) for a cubic polynomial $ \ f (x) \ = \ ax^3 + bx^2 + cx + d \ \ $ and its point of inflection has already been resolved by Z Ahmed It may be of interest to consider why such a simple relation holds true Since the constant term $ \ d \ $ only affects the "vertical" position of the graph for $ \ f (x
Prove: If there is just one critical number, it is the abscissa at the . . . I've answered the first part by using the quadratic formula to get the critical numbers of the first derivative and taking the average, which gives $\frac {-b} {3a}$, which is the same as the abscissa of the inflection point obtained by setting the second derivative to zero I can't figure out how to prove the second part