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find the coordinates of the turning points of the curve y = 2x^4-4x^3+3, and determine the nature of these points

To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and setting t...
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Answered by Jenny N. • Maths tutor
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A circle has equation x^2+y^2-8x+10y+41=0. A point on the circle has coordinates (8,-3). Find the equation of the tangent to the circle passing through this point.

From the equation x 2 +y 2 -8x+10y+41=0, we can find the centre of the circle by the middle two terms -8x+10y and multiplying them by -1/2. So the coordinates of the circle centre are (4,-5).Now we can find ...
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Answered by Joseph K. • Maths tutor
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In trigonometry , how do you find the angles of a right angle triangle?

In order to do that, and this only works for right angled triangles, is using the sine, cosine, and tangent rules. An easy way to remember this is by using the acronym SOH, CAH, TOA that my teacher taught us...
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Answered by Paulina W. • Maths tutor
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Solve: 4(3x − 2) = 2x - 5

The question is asking us to find the value of x. First, we need to multiply the brackets out. To do this, multiply everything in the bracket by 4 so 4 3x=12x and 4 -2=-8 this gives the equation 12x - 8 = 2x...
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Answered by Ellecia S. • Maths tutor
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The equation kx^2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. Show that k satisfies k^2-5k+4>0.

This questions is a proof type question, which means that you need to get to a specific formula. Usually, these questions give you clues in order to prove it. In this case it tells you that the equation has ...
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Answered by Alin G. • Maths tutor
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