Let f(x) = x^3 - 12x. Which statement about this function is false?

a. the function has one inflection point


b. the function is concave upward for x%26gt;0


c. the function has two relative extrema


d. the function is increasing for values of x between -2 and 2


e. the function has a relative minimum at x=2Let f(x) = x^3 - 12x. Which statement about this function is false?
answer is d


If you want a quick answer go to last couple sentances





f ' (x)= 3x^2 -12


set this equal to zero for the critical points and we obtain





x=+-2





f ''(x)=6x





Plug in the values


x=2 we have 12=+


x=-2 we have -12=-





remember that if:


2nd derivative is 0 we have an inflection point


2nd derivative is + we have a concave up graph and a relative minimum


2nd derivative is - we have a concave down graph and a relative maximum





Observing the resluts of plugging in the critical points x=2 and x=-2 it is clear that b,c, and e are satisfied. Because the concave changes between x=-2 and x=2, there must be an inflection point between the two and we know that it is x=0 since that satisfies f ''(x)=6x=0, So we have one, and only one inflection point.





Now we see that the only statement not satisfied is d this makes sense since x=-2 is a maximum the region x=-2 =%26gt; x=2 must be decreasing rather than increasing.


I hope I didn't make a simple problem appear needlessly complicated.Let f(x) = x^3 - 12x. Which statement about this function is false?
d
e i think