What is the equation ?
1 answer:
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The function
... f(x) = (x+2)/(x-1) = 1 + 3/(x-1)
is symmetrical about the line y=x, hence is its own inverse.
We can evaluate the desired derivative directly.
... f'(x) -3/(x-1)²
so f'(2) is
... f'(2) = -3/(2-1)²
If one of our zeros is 4, then the factor is x-4. If the second zero is 5i, then the conjugate root theorem says there HAS to be a root that is -5i. So our 3 factors are (x-4)(x+5i)(x-5i). We will FOIL out these factors to get the polynomial. Let's start with the ones that contain the imaginary numbers. Doing that mutliplication we get x^2-25i^2. i^2 is equal to -1, so what that expression simplifies down to is 
. Now we will multiply in that last factor of (x-4): 
. FOILing out we have 
. There you go!