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

Guest Nov 24, 2018

#1**+1 **

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

CPhill Nov 24, 2018