Quotient rule question

Hi can someone check my working out for part a and b and then help me with part c please? :smile:

ai) you get the soln so it looks ok
aii) Have a read
https://www.mathsisfun.com/calculus/concave-up-down-convex.html
It obviously uses part a)

Upload what youve tried for b?

(edited 2 years ago)

Reply 2

akawesome

Original post by mqb2766

a) you get the soln so it looks ok
b) Have a read
https://www.mathsisfun.com/calculus/concave-up-down-convex.html
It obviously uses part a)

Upload what youve tried for c?

B) x>0 i think
I remember something about sinx integrating to root 1+2x i think but i wasnt sure and part c completely threw me

(edited 2 years ago)

Reply 3

mqb2766

Original post by akawesome

I remember something about sinx integrating to root 1+2x i think but i wasnt sure and part c completely threw me

Youre told the substitution for the integral (b)? Part c) is not uploaded.

Reply 4

akawesome

Original post by mqb2766

Youre told the substitution for the integral (b)? Part c) is not uploaded.

Yeah sorry i meant part b

Reply 5

mqb2766

Original post by akawesome

Yeah sorry i meant part b

Just use the suggested substitution and upload what you get to. Generally integrals and derivatives using tan use the tan-sec identity at some point.

Reply 6

mqb2766

Original post by akawesome

B) x>0 i think
I remember something about sinx integrating to root 1+2x i think but i wasnt sure and part c completely threw me

aii) didnt comment on it, but redo your working and check it. It sounds like the curve is given to you, so just eyeball it for a rough verification. You could note that the function is symmetric about x=0, so it must have the same properties on each side. Based on this, your guess isnt correct.

Reply 7

akawesome

Original post by mqb2766

Just use the suggested substitution and upload what you get to. Generally integrals and derivatives using tan use the tan-sec identity at some point.

Hi I tried it and i got this

Reply 8

akawesome

Original post by mqb2766

Would it be the function is concave downwards for all real values of x?

(edited 2 years ago)

Reply 9

mqb2766

Err youve forgotten to change the dx to a dtheta? Its one of the fundamental parts of integration by substitution. Similarly the theta reverts to x and the limits dont change ....

Reply 10

akawesome

Original post by mqb2766

Err youve forgotten to change the dx to a dtheta? Its one of the fundamental parts of integration by substitution. Similarly the theta reverts to x and the limits dont change ....

So would the answe be cos^-1 of the final answer that i got?

(edited 2 years ago)

Reply 11

mqb2766

Original post by akawesome

Would it be the function is concave downwards for all real values of x?

Why not do the analysis properly (second derivative sign) based on the info in that link and verify it with your ruler using the figure given in the question, as is described at the top of the link.

Reply 12

mqb2766

Original post by akawesome

So would the answe be cos^-1 of the final answer that i got?

No. Line 1 has several mistakes which wont simply disappear by taking acos. You really need to redo a few worked examples of substition from your textbook.