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

   Reply