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calculus

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find an equation of the tangent line to the curve y = x √x that is parallel to the line y = 1 + 3x.

  • calculus - ,

    y
    =f(x)
    =x√x
    =x3/2
    Use the power rule for derivatives to get
    f'(x)=(3/2)√x

    For L: y=3x+1, the slope is 3.

    Solve for x0 in
    f'(x0)=3

    Find the ordinate
    y0=f(x0)

    The point of tangency is therefore at (x0,y0).

    Now pass a line L1 through (x0,y0) having a slope of 3:
    (y-y0)=3(x-x0)

    Check that the line has a slope of 3 and pass through the point (x0,y0)

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