By the quotient rule, your derivative should be . The evaluation of the x values of critical points is correct though. Note that f(-8) = -3/48 = -1/16 and f(-2) = -3/12 = -1/4. How did you determine which is a local max and which is a local min?
So far this is what i got:
Original eq:
f(x)=(x+5)/(x^2-16)
By using quotient rule i got:
f'(x)=0=x^2-16-2x^2-10x
0=(x+8)(x+2)
x=-8, x=-2
Now subbing them back into f(x) i got max and min as (correct me if im wrong):
(-8,3/80) and (-2, -3/20)
Point of inflection:
f''(x)=2(x^3+15x^2+48x+80)/(x^2-16)^3
the second derivative is right im pretty sure i just took out 2 as common factor:
Now this is where im confused do i make the whole thing equal 0, or the top line? and how can i simplify it afterwards?
By the quotient rule, your derivative should be . The evaluation of the x values of critical points is correct though. Note that f(-8) = -3/48 = -1/16 and f(-2) = -3/12 = -1/4. How did you determine which is a local max and which is a local min?