Find the slope of the tangent line to the curve f(x) = x – 2/(x-1)(x+3) when x = 0.
a) 2/3
b) 1/9
c) 7/9
d) –(7/9)
2007-05-11 03:24:23 · 2 answers · asked by Full of Questions 1 in Science & Mathematics ➔ Mathematics
When we try to find the slope of he tangent line, we mean to find the derivative of the function when x=0.
Thus. f(x) = x – 2/(x-1)(x+3)
Using (udv -vdu) / v^2
[(x^2+2x-3)(1) -(x-2)(2x+2)] / (x^2+2x-3)^2
f'(x)= (-x^2+4x+1) / (x^2 + 2-3)^2
thus, f'(0) =1/9.
Letter b.
2007-05-11 04:03:38 · answer #1 · answered by kpgkn29 2 · 0⤊ 0⤋
1) find the slope (it will be an equation) by differentiating the equation.
This is a case of f(x) = u/v (u= x-2) (v= (x-1)(x-3) )
f'(x) = (u'v - uv')/v^2
2) replace x by 0 in the differential
f'(0) = ?
2007-05-11 10:30:48 · answer #2 · answered by Raymond 7 · 0⤊ 0⤋