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

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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