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Prove that the equation y = 3x^4 - 8x^3 - 3 has a turning point at x=2

By definition, turning points occur when the gradient function equals to zero. To prove this we need to differentiate the function given. To differentiate, bring the power down and multiply it by the co-effi...
Answered by • Maths tutor
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Find the gradients of y = 3x^2 − (2/3) x + 1 at x = 0

y = 3x^2 − (2/3) x + 1Derivative of 3x^2 = 6x3 * 2 = 6x^(2-1) = x^1 = xDerivative of -(2/3)x = -2/3-(2/3) * 1 = -2/3x^(1-1) = x^0 = 1dy/dx = 6x - 2/3at x = 0dy/dx = 6(0) - 2/3dy/dx = -2/3
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Answered by Zaid B. • Maths tutor
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How do I integrate fractions of quadratic or cubic terms?

Whenever you see fractions of x or x 2 etc top or bottom, your first port of call would have to be to convert them into partial fractions. Once you have done this, the questions you would get would allow for...
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Answered by Afrose A. • Maths tutor
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What's the proof for the quadratic formula?

Mathematics is a unique subject within which many equations that you encounter have lots of functions and can be derived from the basics. The quadratic formula for instance is incredibly useful to quickly so...
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Answered by Azeem O. • Maths tutor
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Express the fraction (p+q)/(p-q) in the form m+n√2, where p=3-2√2 and q=2-√2.

To answer this question, m and n should be whole numbers instead of fractions, without any square root terms in them. To do this, we first find the numerator, p+q, and the denominator, p-q, individually.Nume...
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Answered by Elizabeth F. • Maths tutor
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