A Triangle Under a Logarithm
Difficulty: Medium · Topics: Calculus, Derivatives, Logarithms
Logarifm ostidagi uchburchak
A point P moves along the curve y=log 2x, with coordinates P(t,\ log 2t), and Q is the foot of the perpendicular from P to the x-axis.
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For the point A(0,\ 1), let S(t) be the area of the triangle PAQ. Find the value of S'(16). (Here t 1.)
P nuqta y=log 2x egri chiziq bo‘ylab harakatlanadi, koordinatalari P(t,\ log 2t), Q esa P dan x o‘qiga tushirilgan perpendikulyar asosi.
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A(0,\ 1) nuqta uchun S(t) — PAQ uchburchak yuzi bo‘lsin. S'(16) ning qiymatini toping. (Bu yerda t 1.)