Calculus

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If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x^3+k, then k is
a: 1/2
b: 1/4
c: 0
d: -1/8
e: -1/2

  • Calculus -

    if y = x^3 + k
    dy/dx = 3x^2 , which of course is the slope of the tangent

    but the slope of the given line is 3/4 , so ...

    3x^2 = 3/4
    x^2 = 1/4
    x = ± 1/2 , but since we are restricted to the first quad,
    x = 1/2
    if x=1/2, 3(1/2) - 4y = 0
    y = 3/8

    The point of contact of the tangent is (1/2 , 3/8)
    so in the cubic ...
    3/8 = (1/8) + k
    k = 3/8-1/8 = 1/4

  • Calculus -

    Thank youu(:

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