How do I derive f(x) = x (sq. rt of) (x + 11)?
f(x) = x(x+11)^1/2 Use product rule to find the derivative.
f '(x)= x[.5(x+11)^-1/2] + (x+11)^1/2 (1)
Then find the second derivative because the point of inflection is ONLY found when setting the second derivative equal to zero. So, after simplifying f '(x) you get f '(x) = (x+2)/[2 (x+11)^1/2] square root of (x+11) is the same as (x+11)^1/2
Take the second derivative and it gives you f ‘’(x) = [2(x+11)^1/2 -(x+2)] / (4(x+11)^1/2)
Now set the second derivative equal to zero to find the point(s) of inflection, and the x-value you get you will plug it into the original function to get the y-value of the exact point of inflection.