Differentiation and Its Application [Edexcel Mathematics B (4MB1) 2014-2016] Topic question

 

1	(Edexcel/Math B/2014/juneR/paper01/q9) Find $\frac{dy}{dx}$ where $y=x^2+\frac6x$	2
2	(Edexcel/Math B/2015/jan/paper01/q2) $y=4x-\frac{1}{2x}$ Find $\frac{dy}{dx}$.	2
3	(Edexcel/Math B/2015/june/paper01/q27) $y=\frac{x}{2}-\frac{1}{2x}$ (a)Find $\frac{dy}{dx}$. (b)Hence find the values of x for which $\frac{dy}{dx}=\frac32-2$	2 5
4	(Edexcel/Math B/2016/jan/paper01/q3) $y=3x^2-\frac3{x^3}$ Find $\frac{dy}{dx}$	2
5	(Edexcel/Math B/2016/janR/paper02/q4) (a)Simplify fully $\frac{2x2-x-10}{3} \times \frac{x}{x+2}$ (b)Given that $y=\frac{2x2-x-10}{3} \times \frac{x}{x+2}$ Solve $\frac{dy}{dx}=0$	3 3
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6	(Edexcel/Math B/2014/jan/paper01/q28) $y=x^3+\frac52x^2-2x+13$ (a)Find$\frac{dy}{dx}$ (b)Hence find the x coordinates of the to stationary points of $y=x^3+\frac52x^2-2x+13$	3 4
7	(Edexcel/Math B/2014/janR/paper01/q16) Given that $y=4x^2-\frac1x$ (a)Find $\frac{dy}{dx}$ (b)Solve $\frac{dy}{dx}=0$	2 2
8	(Edexcel/Math B/2014/juneR/paper02/q11) Figure 3 shows a metal box with no top. The four sides and the base of the box are to be cut from a single rectangular sheet of metal of width x cm as shown in Figure 4. Assuming that no metal is wasted when the box is made, find an expression, in terms of x and y for (a) the length, in cm, of the sheet of metal, (b) the area, in $cm^2$, of the sheet of metal  The area of the sheet of metal is S $cm^2$ and the volume of the metal box is 40 $cm^3$. (c)show that $S=x^2+\frac{160}{x}$ (d) Find, by differentiating, the value of x for which the area of the metal sheet is a minimum. Give your answer to 1 decimal place. (e)For $=x^2+\frac{160}{x}$, complete the following table giving your values of S to one decimal place where necessary (f) On the grid opposite, plot the points from your completed table and join them to form a smooth curve. (g) Using your curve, find a value of x when S = 75	1 1 2 4 3 3 2
9	(Edexcel/Math B/2015/juneR/paper02/q5) The curve C has equation $y=x-\frac{4}{x}$ Find $\frac{dy}{dx}$ Find the coordinates of the point on C at which the gradient is 17.	2 4
10	(Edexcel/Math B/2016/jan/paper01/q17) A curve has a equation $y=5x^2-6x+15$ . Find the x coordinate of the point on the curve at which the gradient of the curve is -2	4
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