Question

Use the equation of the tangent line at x=2 to approximate f(2.03) for f(x)= ln(cuberoot(x+1)). Your work must include the equation of the tangent line using exact values. Give 3 decimal places in your final answer.

Answer 1

can you differentiate f(x) = ln (x+1)^(1/3)?

Answer 2

yes

Answer 3

1/3x+3

Answer 4

right - so that's the slope of the tangent to the curve
so can you find the equation of the tangent at x = 2?

Answer 5

oh ok I see what to do now, I just didn't know what I needed to do. So the equation of the tangent is y=x/9+7.288/9

Answer 6

then I assume I would just plug in x?

Answer 7

yes

Answer 8

brilliant, thanks

Answer 9

I also have another question about inverses. you don't have to answer it for me, I just don't know where to start.-
Full question-
If h-1 is the inverse function of h, with the values of h and h '(x) given in the table below, find the slope of the line tangent to the graph of y = h-1(x) at x = 3.
Table-
x h(x) h'(x)
6 3 7
8 4 6

Answer 10

sorry gotta go right now

Answer 11

ok thanks for your help!