- #1
JackieAnne
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Let f(x)=x^6ln(x) . Find (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.
(a) f is increasing on the interval(s)
(b) f is decreasing on the interval(s)
(c) f is concave up on the open interval(s)
(d) f is concave down on the open interval(s)
(e) the x coordinate(s) of the points of inflection are
Notes: In the first four boxes, your answer should either be a single interval, such as [0,1), a comma separated list of intervals, such as (-inf, 2), (3,4], or the word "none".
In the last box, your answer should be a comma separated list of x values or the word "none".
So, I am pretty sure for concave functions we are supposed to find the first and second derivatives.
I am unsure about the first derivative but I got:
(1/7)x(-1/7)*(1/x)
I am unsure on how to get the second derivative from this. Then unsure how to solve the rest of this problem. Thanks!
(a) f is increasing on the interval(s)
(b) f is decreasing on the interval(s)
(c) f is concave up on the open interval(s)
(d) f is concave down on the open interval(s)
(e) the x coordinate(s) of the points of inflection are
Notes: In the first four boxes, your answer should either be a single interval, such as [0,1), a comma separated list of intervals, such as (-inf, 2), (3,4], or the word "none".
In the last box, your answer should be a comma separated list of x values or the word "none".
So, I am pretty sure for concave functions we are supposed to find the first and second derivatives.
I am unsure about the first derivative but I got:
(1/7)x(-1/7)*(1/x)
I am unsure on how to get the second derivative from this. Then unsure how to solve the rest of this problem. Thanks!