Find an equation of the tangent line to the graph of the function at the given point y=4-ln(1/2x+1) , point (0,4)

Question

Find an equation of the tangent line to the graph of the function at the given point y=4-ln(1/2x+1) , point (0,4)

Answer 1

Step 1: Find the slope of the equation.

m = (4 - ln(1/2x + 1))'

m = -1/2(1/2x + 1)^(-1)

At the point (0, 4), x = 0, so:

m = -1/2(1/2*0 + 1)^(-1)

m = -1/2(1)^(-1)

m = -1/2

Step 2: Find the equation of the tangent line.

y - y1 = m(x - x1)

y - 4 = -1/2(x - 0)

y - 4 = -1/2x

y = 4.75x - 4