Find the equation of the tangent line to the graph of f(x) = 6x ln(x + 4) at x = 2.

Answer 1

dy/dx = 6x d/dx [ln(x+4)]+ 6 ln(x+4)

= 6 x /(x+4) + 6 ln(x+4)
so at x = 2
dy/dx = slope = m = 12/ln(6) + 6 ln (6)

but ln (6) = 1.79
so use that to find the slope m

then we have
y = m x + b and we know m

find y at x = 2
y= 12 (1.79) = 21.5
so use that
21.5 = 2 m + b
we know m, solve for b
the end

Answer 2

Thank you!

Answer 3

You are welcome.