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A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

^dy/_dx = 9x^2 + 2ax + b

x = 2, ^dy/_dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, ^dy/_dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

Answered by Alistair R. • Further Mathematics tutor

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How do I know when I should be using the Poisson distribution?

To identify a Poisson distribution question, remember that in a Poisson distribution... Events occur independently of each other Events occur at a constant rate Events occur singly (that is, two can't hap...

Answered by Hannah D. • Further Mathematics tutor

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Why does matrix multiplication seem so unintuitive and weird?!

You're right, when you first learn about matrix multiplication it definitely doesn't feel like the easiest way of defining a form of multiplication. This is particularly true if you've just lear...

Answered by Daniel C. • Further Mathematics tutor

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A curve has equation y=(2-x)(1+x)+3, A line passes through the point (2,3) and the curve at a point with x coordinate 2+h. Find the gradient of the line. Then use that answer to find the gradient of the curve at (2,3), stating the value of the gradient

The gradient of the line is given by change in Y divided by change in X. To find the Y value of the point we must put 2+h into the y=(2-x)(1+x)+3. Doing this we get y=(2-(2+h))(1+(2+h))+3=(-h)(3+h)+3= -3h...

Answered by James C. • Further Mathematics tutor

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