f(x) = (x)/[(x^2 + 4)]
Locate all inflection points
I got f'(x) = (-x^2 + 4)/[(x^2 +4)]^2
and found f''(x) = [2x(x^4 - 8x^2 - 48)]/[(x^2+4)^4]
x = 0, 4i, some other number
I'm sure theres an easier way of finding the second derivative, any help guys?
You can make the second differentiation slightly simpler by applying the product rule directly, but in a diagram. Straight continuous lines differentiate (downwards) with respect to x, in this pattern:
Or, zooming in further... we can see the chain rule telling us to differentiate down the straight dashed line with respect to the inner function i.e. with respect to the dashed balloon:
(Then multiply out the balloons as brackets and make (x^2 + 4)^3 a common denominator.)
Hope this helps. Use it for integration too - see Balloon Calculus: worked examples from past papers,
and a similar thread http://www..com/math-help/calculus/5...erivative.html