How would you find the inflection point and the concavity of #g(x) = (5x - 2.6) / (5x - 6.76)^2#? I know I have to take the 2nd derivative but i'm not sure how because of the odd way this function is set up.?

1 Answer
Apr 24, 2015

Use the quotient rule to find #g'(x)#, then simplify if possible, then use the quotient rule again to find #g''(x)#.

#g(x)= (5x-2.6)/(5x-6.76)^2#

#g'(x)=( 5(5x-6.76)^2 - (5x-2.6)2(5x-6.76)(5))/(5x-6.76)^4#

# = ( 5(5x-6.76)[(5x-6.76) - 2(5x-2.6)])/(5x-6.76)^4#

# = ( 5[5x-6.76 - 10x + 5.2])/(5x-6.76)^3#

#g'(x) = ( -5(5x + 1.56))/(5x-6.76)^3#

Differentiate again to get #g''(x)#.

After finding #g''(x)#, proceed as in any other question about concavity.