Tangent Lines

If f(x)= [(-x/9) + (1/6)] SQRT(-12x-9)
and g(x)= -x-6

how would you find the tangent line of f(x) that is parallel to g(x)?
I know you would find the first derivative of f(x), but then I don't know where to continue on to.

Reply 1

dpm

Original post by PatchworkTeapot

(i) What is the gradient of g(x), call it m.
(ii) set f'(x) equal to the answer from (i)

solve (ii) and this will tell you the x value of the point on f(x) for which the gradient is the same as that of g(x) .. (and hence the tangent at the point is parallel to g(x)). lets calls this value k.

iii) find f(k) to find the corresponding y - value.

you now have the required point on f(x); namely (k,f(k)) and its gradient, m.

now find the equation of the tangent line:

(e.g. y-f(k)=m(x-k))