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A curve is described by f(x) = x^2 + 2x. A second curve is described by g(x) = x^2 -5x + 7. Find the point (s) where both curves intersect.

To find the points where two curves meet a difference function needs to be calculated. This function is formed by subtracting one function from the other: d(x) = f(x) - g(x). It also works the other way a...

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A curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx and d2y/dx2. Verify C has a stationary point at x = 2. Determine the nature of this stationary point, giving a reason for the answer.

y = 3x⁴- 8x³- 3Bringing the power down on each term and subtracting one from the power (as to differentiate, nx^m —> nmx^m-1), we get for each derivative:dy/...

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Find the x values for stationary points in the curve y=3sin(2x) for 0<x<180

Firstly we differentiate the equation y=3sin(2x) w.r.t. x.By using the chain rule, we find the dy/dx=6cos(2x)Since a stationary point in the curve is a point where the gradient is 0, we can find them by f...

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find dy/dx when y=x^3 + sin2x

so this question is asking you to differentiate x³ + sin2xwe know that xⁿ differentiates do nx^n-1, so using that x³ will differentiate to 3x²we know ...

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Ignoring air resistance and assuming gravity to equal 9.81. If a ball of mass 1kg is dropped from a height of 100m, calculate it's final velocity before it hits the ground.

G = 9.81u = 0s = 100v²= u²+ 2asv²= 2 * 100 * 9.81v = root( 2 * 100 * 9.81) = 44.29ms^-1
This question can be made into a 3 part question suitable for adv...

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