Question

Let f and g be differentiable functions with the following values:
f(1) = 2 f'(1) = 3 g(1) = 2 g'(1) = -3
f(2) = 4 f'(2) = -4 g(2) = -5 g'(2) = 5
If h(x)=1/(g(f(x))), write the equation of the line tangent to h at x =1



so far, I've got
\[h'(x) = \frac{ -(g'(f(x))*f'(x) }{ (g(f(x)))^{2}}\] and
\[h'(1) = -\frac{ 3 }{ 5 }\] I am not sure how to get the equation of the line though...

Answer 1

to find equation of a line, you'll need a slope and a point
slope = h'(1) = -3/5
find the point,
when x= 1, h(1) =... ?

Answer 2

then the point is just (1,h(1))

Answer 3

oh, okay thank you!
I get it now :D

Answer 4

welcome ^_^