Posted by unknown on Sunday, October 2, 2011 at 5:02am.
Find the interval(s) where the function is increasing of decreasing.
a) critical value(s)
b) critical point(s)
c) max. value + max. point
d) min.value and min. point
e)point on inflection if there is:
- Diff Calculus - Reiny, Sunday, October 2, 2011 at 8:44am
A rather uninspiring graph
There is an obvious y-intercept of 12
after trying the usual methods of finding some f(a) = 0
I used WolframAlpha to see what we had
It showed no x-intercepts, thus no solution for f(x) = 0 , but rather 4 complex roots
I then clicked on the derivative expression to get one real root at appr x = .6
f(.6) = .6^4 - 3(.6)^3 + 22(.6)^2 - 24(.6) + 12 = appr. 5
So there is a turning point at about (0.6 , 5)
clicking on the derivative of that cubic shows that the resulting quadratic has no real roots, thus no points of inflection
(It would have been a nightmare to attempt this without some convenient software, solving this with only pencil and paper and a basic calculator seems daunting )
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