Question

determine the equation of the tangent line to f(x)=15+8ln(x) at x=1

Answer 1

\[\huge f(x)=15+8lnx \]
\[\huge f'(x)=8[lnx]' = \frac{8}{x}\]

Answer 2

so at x=1, f'(1) = 8/1 = 8.. this is slope of the tangent line...
f(1) = 15 + 8*ln1 = 15 + 8*0 = 15
so the graph goes through (1, 15)

now that you have a point and the slope of the tangent line, put it in point-slope form to get equation of the tangent line.

Answer 3

point-slope form:
\[\huge y-y_0=m(x-x_0) \]
\[\huge y-(15)=8(x-(1)) \]
\[\huge y-15=8(x-1) \]
this is the equation of your tangent line...

Answer 4

thank you very much your a great help