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March 26, 2017

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Find the value of c where the line l tangent to the graph of y=2.5*5^x at (0,2.5) intersects the x-axis

  • Calculus - ,

    dy/dx = 2.5(5^x)ln5
    when x=0 from (0, 2.5)
    dy/dx = 2.5ln5

    so tangent is y= 2.5ln5 x + c
    at (0 , 2.5)
    2.5 = 0 + c
    so the equation is y = 2.5ln5 x + 2.5
    at the x-axis, y =0
    0 = 2.5ln5 x + 2.5
    2.5ln5 x = -2.5
    ln5 x = -1
    x = -1/ln5 or appr -.62

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