Question

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

Answer 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