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Find the coordinates of the minimum point on the curve: y = x^2 - x - 2

Start with the given equation from the question and differentiate it with respect to x to give you:dy/dx = 2x - 1The value of this gives you the slope of the curve and we know that the minimum point has a...

Answered by Alex R. • Maths tutor

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A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.

We know that a stationary point is found when the gradient of the curve is equal to zero, this is found by equaling the derivative (dy/dx) equal to zero. Differentiating the expression will find a quadrat...

Answered by Georgia S. • Maths tutor

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Solve the equation (x+2)/(x-3)=(x-6)/(x+1) for x.

We need to multiply both sides by the denominator (the bottom of the fraction) in both fractions so we get:(x+2)(x-3)(x+1)/(x-3)=(x-6)(x-3)(x+1)/(x+1)Now, we can see that we can cancel each fraction to ge...

Answered by Tom H. • Maths tutor

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Consider the infinite series S=Σ(from n=0 to infinite) u(down n) where u(down n)=lim (from n π to (n+1) π) ((sin t)/t) dt. Explain why the series is alternating.

For the first part of the question we need to try and understand what is actually happening – we have the sum of an integral – where we are summing a sequence of definite integrals. So when n = 0 we have ...

Answered by Stuart D. • Maths tutor

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