Hrishi98 Posted January 16, 2015 Report Share Posted January 16, 2015 (edited) (b) The function f is defined by f (x) = x2 + 4 cos x for 0 < x < π.(i) By considering the graphs of y = x and y = 2 sin x, show that f (x) has only one stationary point, and explain why this stationary point is between pi/2 and π.(ii) Find f ″(x) and hence prove that the stationary point is a minimum.(iii) Find the coordinates of the point of inflection on the graph of y = f (x).(iv) Sketch the graph of y = f (x), clearly labelling the stationary point and the point of inflection. I have found the answer, but im not sure whether its right. Edited January 16, 2015 by Hrishi98 Reply Link to post Share on other sites More sharing options...
Vioh Posted January 16, 2015 Report Share Posted January 16, 2015 (b) The function f is defined by f (x) = x2 + 4 cos x for 0 < x < π.(i) By considering the graphs of y = x and y = 2 sin x, show that f (x) has only one stationary point, and explain why this stationary point is between pi/2 and π.(ii) Find f ″(x) and hence prove that the stationary point is a minimum.(iii) Find the coordinates of the point of inflection on the graph of y = f (x).(iv) Sketch the graph of y = f (x), clearly labelling the stationary point and the point of inflection. I have found the answer, but im not sure whether its right. I don't know whether this is a calculator question or not. But i'll assume it's not. Here is my full worked solution (pay attention to the stuff that I typed in bold): I realized that the last part looks rather complicated. To be honest, you can simply sketch f(x) based on intuition. However if you want to see the mathematical reasoning behind it, then just look at my solution. If there's anything unclear, feel free to ask! 1 Reply Link to post Share on other sites More sharing options...
Hrishi98 Posted January 18, 2015 Author Report Share Posted January 18, 2015 (b) The function f is defined by f (x) = x2 + 4 cos x for 0 < x < π.(i) By considering the graphs of y = x and y = 2 sin x, show that f (x) has only one stationary point, and explain why this stationary point is between pi/2 and π.(ii) Find f ″(x) and hence prove that the stationary point is a minimum.(iii) Find the coordinates of the point of inflection on the graph of y = f (x).(iv) Sketch the graph of y = f (x), clearly labelling the stationary point and the point of inflection. I have found the answer, but im not sure whether its right. I don't know whether this is a calculator question or not. But i'll assume it's not. Here is my full worked solution (pay attention to the stuff that I typed in bold): Untitled.png I realized that the last part looks rather complicated. To be honest, you can simply sketch f(x) based on intuition. However if you want to see the mathematical reasoning behind it, then just look at my solution. If there's anything unclear, feel free to ask! This was a great help to me as I was stuck in the graph question, cause it was rather complicated. But, I viewed through graphs and agree with the conclusive answer you provided Reply Link to post Share on other sites More sharing options...
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