we know that
Points of inflection can occur where the second derivative is zero
we have
f(x)=(x-2)/(x-5)
Find the First derivative
f'(x)=1/(x-5)+(x-2)(-1)(x-5)^-2
f'(x)=1/(x-5)-(x-2)/(x-5)^2
Find the second derivative
f''(x)=(-1)(x-5)^-2-1/(x-5)^2-(2)(x-2)(x-5)^-3
f''(x)=-1/(x-5)^2-1/(x-5)^2-2(x-2)/(x-5)^3
f''(x)=-2/(x-5)^2-2(x-2)/(x-5)^3
equate the second derivative to zero
0=-2/(x-5)^2-2(x-2)/(x-5)^3
2/(x-5)^2=-2(x-2)/(x-5)^3
Multiply both sides by (x-5)^3
2(x-5)=-2(x-2)
solve for
