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The function f(x)=x^2 -2x -24x^(1/2) has one stationary point. Find the value of x when f(x) is stationary, and hence determine the nature of this stationary point.

dy/dx = 2x - 2 -12x -1/2 dy/dx = 02x - 2 - 12x -1/2 = 0x = 4 (stationary point)d 2 y/dx 2 = 2 + 6x -3/2 when x=4, d 2 y/dx 2 = 11/411/4 > 0 therefore the point is a minimum
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A curve has an equation of y=2x^2 + 7x -8 . Find the co-ordinates of the turning point

Student will need to understand that the turning point will be a minimum as the curve is positiveStudent should complete the square:1) factorise out the 2: 2(x 2 + 7/2 x) - 82) complete the square : 2[(x+7/4...
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Answered by Farah H. • Maths tutor
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Take the 2nd derivative of 2e^(2x) with respect to x.

The second derivative is just two derivatives carried out back to back. In this case we just have to differentiate this function once, and then differentiate the result. The derivative of 2e^(2x) can then be...
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Answered by Patrick A. • Maths tutor
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What is a logarithm?

Logarithms, written in the form log x y, are another type of mathematical 'operation', just like addition or multiplication. Subtraction as the opposite of addition, division is the opposite of multiplicatio...
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Answered by Laurie H. • Maths tutor
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Consider f (x) = logk (6x - 3x 2 ), for 0 < x < 2, where k > 0. The equation f (x) = 2 has exactly one solution. What is the value of k?

There are two essential tricks to grasp in this question. Firstly, since the equation has only one solution, the Discriminant that will be required would equal 0. Secondly, since we are given f(x) = 2 we can...
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Answered by Jaroslav S. • Maths tutor
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