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Given that y = 16x + x^-1, find the two values of x for which dy/dx = 0

Expected layout of answer in an exam: y = 16x + x -1 dy/dx = 16 - x -2 dy/dx = 0 implies that 16 - x -2 = 0this implies that 16 = x -2 16 = 1/x 2 16x 2 = 1x 2 = 1/16therefore x = +/- 1/4x = 1/4, x = -1/4 whe...
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Answered by Sawdah H. • Maths tutor
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How do I differentiate?

If we have the curve y=x 3 +3x 2 -7x+5, to differentiate it we firstly multiply x by its power, and then reduce the power by one.Therefore x 3 will differentiate to 3x 2 , 3x 2 will go to 6x and -7x will go ...
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Answered by William H. • Maths tutor
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Given y = 2x(x^2 – 1)^5, show that dy/dx = g(x)(x^2 – 1)^4 where g(x) is a function to be determined.

y=2x(x 2 -1) 5 dy/dx= 2(x 2 -1) 5 + 2x*10x(x 2 -1) 4 dy/dx=(x 2 -1) 4 (2x 2 -2+20x 2 )dy/dx=(x 2 -1) 4 (22x 2 -2)
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Answered by Katie S. • Maths tutor
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A small stone is projected vertically upwards from a point O with a speed of 19.6m/s. Modelling the stone as a particle moving freely under gravity, find the length of time for which the stone is more than 14.7 m above O

We want to find out the time during which the stone is above a certain point. As this stone is thrown upwards we know that the first time it passes this point it will be on its way up and when it passes the ...
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Answered by Aaron G. • Maths tutor
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How do you differentiate the curve y = 4x^2 + 7x + 1? And how do you find the gradient of this curve?

To begin with, this question requires you to differentiate the curve y = 4x 2 + 7x +1 in order to find the gradient. To differentiate this function y in respect to x, we need to reduce the powers by one, for...
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Answered by Katie S. • Maths tutor
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