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The curve with the equation: y=x^2 - 32sqrt(x) + 20 has a stationary point P. Find the coordinates of P.

A stationary point implies that the gradient at this point will be equal to 0, it is a turning point in the graph. So we need to find the value of X at which dy/dx = 0. [where dy/dx is the gradient.]So we fi...
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Answered by Maninder B. • Maths tutor
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Solve the equation 2(cos x)^ 2=2-sin x for 0 <=x<=180

Recall the identity ((cos x)^2+(sin x)^ 2=1). Rearrange the identity to give cos x in terms of sin x. Substitute this into the equation. Rearrange so all terms are on one side of the equation and factories t...
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Answered by Pablo G. • Maths tutor
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If I had an equation with both 'x' and 'y' present, how would I find the gradient?

Using the equation (x+y) 2 =xy 2 as an example base to see how it would work in practice. The most important fact is that dy/dx =y' . Simply put, the derivative of y is dy/dx. This allows you to go through a...
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Answered by Oli K. • Maths tutor
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Why, how and when do we use partial fractions and polynomial long division?

Partial fractions and long division have the same purpose which is to decompose complex expressions into simpler ones in order to easily deal with them in calculations. Think of them as tools that we use for...
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Answered by Daniel W. • Maths tutor
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Differentiate y= (3x^2+2x-6)^8

This is an example of where we must use the chain rule: Firstly as with simpler differentiation we multiply the function by the power then subtract 1 from the power to get: 8(3x^2+2x-6)^7 Then we must also m...
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Answered by Ollie T. • Maths tutor
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