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 February 9th, 2018, 10:23 AM #1 Senior Member   Joined: Sep 2011 Posts: 104 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: 7,689 Thanks: 2669 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 Senior Member   Joined: Sep 2011 Posts: 104 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: 2,571 Thanks: 1415 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Lazar Calculus 1 December 28th, 2014 12:40 PM charmi Calculus 4 December 31st, 2013 04:07 PM charmi Calculus 3 December 31st, 2013 02:36 PM faraday007 Calculus 1 January 23rd, 2011 03:05 AM MathematicallyObtuse Calculus 8 November 3rd, 2010 01:26 AM

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