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A curve is defined for x > 0. The gradient of the curve at the point (x,y) is given by dy/dx = x^(3/2)-2x. Show that this curve has a minimum point and find it.

This is a typical exam style question, taken from an AQA paper. This question is testing your knowledge of stationary points and differentiation. Step 1: Find all stationary points by setting the first ...

Answered by Yishuang C. • Maths tutor

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The circle (x-3)^2 +(x-2)^2 = 20 has centre C. Write down the radius of the circle and the coordinates of C.

Radius = square root of 20
Centre = (3,2)

Answered by Jessica N. • Maths tutor

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What is the exact answer to (1^3 + 2^3 + 3^3)^(0.5) ?

+6 or -6

Answered by Jessica N. • Maths tutor

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Given y=2x^4-1+x^1/2, solve dy/dx

Using the sum rule, you can split the function in three terms and then derive each of them separately. The rule is to bring down the power and the power minus one. So for the first term, it becomes 2*4x

Answered by Yanni C. • Maths tutor

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How do I find a stationary point on a curve and work out if it is a maximum or minimum point?

At any stationary point, the gradient of a line is zero.
Therefore dy/dx = 0. If we differentiate the equation of the line, and solve this expression we can find the coordinates of the stationary po...

Answered by Benjamin H. • Maths tutor

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