+318 Find the critical values there should be 3:
f(x)= (3x^2 +3x +6 )/ (x^2+x-56)
help????? i already got -1/2, and -7/75
+9673 \(f(x) = \dfrac{3x^2 + 3x + 6}{x^2 + x - 56} = 3 - \dfrac{58}5 \left(\dfrac{1}{x + 8} - \dfrac1{x - 7}\right)\)
Differentiating, \(f'(x) = \dfrac{58}5\left(\dfrac1{(x + 8)^2} - \dfrac1{(x - 7)^2}\right)\)
When \(f'(x) = 0\),
\((x - 7)^2 - (x + 8)^2 = 0\\ 2x + 1 = 0\\ x = -\dfrac12\)
Also, \(f\left(-\dfrac12\right) = -\dfrac7{75}\), so the critical point is \(\left(-\dfrac12, -\dfrac7{75}\right)\), and there is only 1 critical point, not 3.
+318 When I enter -1/2 it says partially correct!! It is asking for another value!
