## Concave Functions

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!

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 Quote by JackieAnne 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!
I'm assuming you mean f(x)=(x^6)*ln(x). Work on your derivative first. It's way wrong. Do you know how to differentiate x^6? Have you heard of the product rule?
 okay, so I think I got the first derivative: 6x^5*ln(x) + x^6*(1/x) so then would the second derivative be: 30x^4*ln(x) + x^6*(-1/x^2)

Recognitions:
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