An Elementary Treatise On the Differential Calculus With Applications And Nume
An Elementary Treatise On the Differential Calculus With Applications And Nume
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18. Show that the chord of a given curve which passes through a given point and cuts off a maximum or minimum area is bisected at the point.
19. Find the area of the greatest triangle which can be inscribed in a given parabolic segment having for its base the bounding chord of the segment.
20. In any oval curve the maximum or minimum chord which is normal at one end is either a radius of curvature at that end, or normal at both ends.
21. In the axis of a given parabola and within the curve are ...taken two fixed points P, Q ; find the point on the curve at which the line PQ subtends the greatest angle, and show that, if the semi-latus rectum is an Arithmetic mean between the distances of P, Q from the vertex, the abscissa of the point is to the geometric mean between the distances as 1 : >J3. [Oxford, 1889 ] 488. Analytical Investigation.
We now proceed to investigate the conditions for the exist- ence of maxima and minima values from a purely analytical point of view.
It appears from the definition given of maxima and minima values that as x increases or decreases from the value a through any small but finite interval h, if cp(x) be always less than
To quickly assess the difficulty of the text, read a short excerpt:
18. Show that the chord of a given curve which passes through a given point and cuts off a maximum or minimum area is bisected at the point.
19. Find the area of the greatest triangle which can be inscribed in a given parabolic segment having for its base the bounding chord of the segment.
20. In any oval curve the maximum or minimum chord which is normal at one end is either a radius of curvature at that end, or normal at both ends.
21. In the axis of a given parabola and within the curve are ...taken two fixed points P, Q ; find the point on the curve at which the line PQ subtends the greatest angle, and show that, if the semi-latus rectum is an Arithmetic mean between the distances of P, Q from the vertex, the abscissa of the point is to the geometric mean between the distances as 1 : >J3. [Oxford, 1889 ] 488. Analytical Investigation.
We now proceed to investigate the conditions for the exist- ence of maxima and minima values from a purely analytical point of view.
It appears from the definition given of maxima and minima values that as x increases or decreases from the value a through any small but finite interval h, if cp(x) be always less than
(a) is a maximum value of
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