Asked by joshua
Determine the interval(s) at which f(x) is concave up given that f′′(x)=−x2+x+6.
Critical points are: -2 & 3
Critical points are: -2 & 3
Answers
Answered by
Reiny
To be concave up the 2nd derivative must be positive, so
-x^2 + x + 6 > 0
x^2 - x - 6 < 0
(x-3)(x+2) < 0
looking at y = x^2 - x - 6 , we see from our solution above that it has x-intercepts of 3 and -2, thus it is above ( greater than zero) for
x < -2 or x > 3
-x^2 + x + 6 > 0
x^2 - x - 6 < 0
(x-3)(x+2) < 0
looking at y = x^2 - x - 6 , we see from our solution above that it has x-intercepts of 3 and -2, thus it is above ( greater than zero) for
x < -2 or x > 3
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