Find an equation of the tangent line to the curve
y=4^x at the point (1,4).

Find an equation of the tangent line to the curve
y=4^x at the point (1,4).

1 thought on “Find an equation of the tangent line to the curve<br />y=4^x at the point (1,4).<br />​”

  1. Answer:

    Equation : 4ln(4)*x – y – 4{ln(4)-1} = 0

    Step-by-step explanation:

    y = 4^x

    The slope of the tangent to a curve at any point is determined by differentiating it w.r.t x,

    dy/dx = (4^x)’

    dy/dx = (4^x)*ln(4)

    m = dy/dx | (1,4) = (4^1)*ln(4) = 4ln(4)

    The tangent passes through (1,4), thus the equation (in one-point form) is :

    (y – 4) = 4ln4(x – 1)

    y – 4 = 4ln(4)*x – 4ln(4)

    4ln(4)*x – y – 4ln(4) + 4 = 0

    4ln(4)*x – y – 4{ln(4)1} = 0

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