What is the tangent point on g(x)=(36/x-1) has an instantaneous rate of change of -9?
That is 36 on the numerator and x-1 on the denomonator
+128407 We can write the function as
f(x) = 36 ( x - 1)^(-1)
The derivative is -36 ( x - 1)^(-2).....set this = - 9
-36(x - 1)^(-2) = -9
36 (x - 1)^(-2) = 9 rearrange as
36/9 = ( x - 1)^2
4 = ( x - 1)^2
The x's that solve this are x = 3 and x = -2
When x = 3....y = 36 / [ 3 - 1] = 18
When x = -2....y = 36 / [ -2 - 1] = -12
So....the two points of tangency are ( 3, 18) and (-2, -12)
Here is the graph : https://www.desmos.com/calculator/pzmmsxfr2z
