![]() |
|
Pre-Calculus Pre-Calculus Math Forum |
![]() |
| LinkBack | Thread Tools | Display Modes |
February 9th, 2018, 10:23 AM | #1 |
Member Joined: Sep 2011 Posts: 97 Thanks: 1 | differentiation / Integration Help
The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q. option 1 : 2.5 option 2: -2.5 option 3: 0 Option 4: -3 I couldn't find the answer from any of the options and will need assistance to how the answer can be obtained. I have substituted x = 0.5 into dy/dx to get the gradient expression of 2 + 4q/5 and integrated to get y = 2x - q/(5x) + c. It seems impossible for me to get the value of q since c could not be found. I am not sure whether the question has some missing information to continue. Your help will be greatly appreciated. Thanks. Last edited by skipjack; February 9th, 2018 at 07:10 PM. |
![]() |
February 9th, 2018, 10:28 AM | #2 |
Math Team Joined: Dec 2013 From: Colombia Posts: 7,268 Thanks: 2434 Math Focus: Mainly analysis and algebra |
What is the value of $\frac{\mathrm dy}{\mathrm dx}$ at a turning point?
|
![]() |
February 9th, 2018, 04:34 PM | #3 |
Member Joined: Sep 2011 Posts: 97 Thanks: 1 |
It was not given to the value of dy/dx.
|
![]() |
February 9th, 2018, 04:59 PM | #4 |
Senior Member Joined: Sep 2015 From: USA Posts: 1,852 Thanks: 959 |
a turning point is where the first derivative of a function changes sign $\dfrac{dy}{dx}=0$ at a turning point. $\dfrac{dy}{dx} = 2+\dfrac{q}{5x^2}$ at $(0.5, -4),~\dfrac{dy}{dx}=0$ $\left . 2+\dfrac{q}{5x^2} \right|_{x=0.5} = 2+\dfrac{q}{5(0.5)^2} = 2+\dfrac{4q}{5} = 0$ $q = -\dfrac 5 2 = -2.5$ i.e. choice 2 |
![]() |
![]() |
|
Tags |
differentiation, ifferentiation, integration |
Thread Tools | |
Display Modes | |
|
![]() | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
recursive integration,integration done, how to get formula | Lazar | Calculus | 1 | December 28th, 2014 12:40 PM |
Integration | charmi | Calculus | 4 | December 31st, 2013 04:07 PM |
Integration | charmi | Calculus | 3 | December 31st, 2013 02:36 PM |
Why this integration comes out to be zero always | faraday007 | Calculus | 1 | January 23rd, 2011 03:05 AM |
Integration | MathematicallyObtuse | Calculus | 8 | November 3rd, 2010 01:26 AM |