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if f(x) = 4x^2 - 16ln(x-1) - 10, find f'(x) and hence solve the equation f'(x)=0.

f(x) = 4x 2 - 16ln(x-1) -10, f'(x) = 8x - 16/(x-1), so if f'(x)=0, then 8x - 16/(x -1)=0, 8x(x-1) - 16 = 0, 8x 2 - 8x - 16 =0, 8(x 2 - x - 2) = 0, x 2 - x - 2 = 0, (x - 2)(x + 1) =0, so x = 2 and x = -1
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Answered by Ellie B. • Maths tutor
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Integrate y=2x^2 +4x-1

To integrate this simple equation add one to the power then divide by the new power for example. 2x^2 becomes 2/3x^3 4x becomes 2x^2 and 1 becomes x plus constant c so the overall integrated equation is 2/3x...
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Answered by George B. • Maths tutor
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Find the exact value of dy/dx at (-2,4) of the curve C: 4x^2 -y^2 + 6xy + 2^y = 0

First notice that this is an equation that will require implicit differentiation since C cannot be explicitly written in terms of either x or y. Thus we must differentiate each term with respect to x:-the fi...
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Answered by Saskia D. • Maths tutor
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You are given the equation y=x^2. Determine whether or not the equation has any maximums or minimums and identify them (whether they are maximums or minimums).

The question has given us a function and wants us to determine whether or not any maximums/minimums exist (and if so identify then). We know maximums/minimums occur when the derivative of the equation is equ...
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Answered by Lana M. • Maths tutor
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Find the area enclosed between the curves y = f(x) and y = g(x)

Don't forget, in order to find the area under a curve y=f(x) between two values x=a and x=b we integrate f(x) between a and b.Thus to find the area enclosed between two curves y=f(x) and y=g(x) we simply nee...
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Answered by Matthew G. • Maths tutor
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