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y = (x^3)/3 - 4x^2 + 12x find the stationary points of the curve and determine their nature.

first we find the first derivative of the function. Here dy/dx = x^2-8x+12. We set this to zero and factorise to obtain the roots of the function. Such that dy/dx = (x-6)(x-2)= 0. This gives the stationary p...
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Answered by Jordan M. • Maths tutor
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Differentiate y = (3x^2 + 1)^2

Looking at this question the first thing we should notice is that there is a an x squared inside a bracket which is also squared. As there is function inside a function we must use the chain rule. The simple...
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Answered by Hannah B. • Maths tutor
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Integrate the following equation to find y: dy/dx = 3x^2 + 2x + 6

Notice that integration is simply the opposite of differentiation. So, if we just integrate this term-by-term then we can find an expression of y in terms of x. So, when we integrate dy/dx becomes y. Integra...
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Answered by Murray M. • Maths tutor
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Find the equation of the straight line that passes through the points (1,2) and (2,4)

Remember that the equation of a straight line (when given two points OR a point and a gradient) is y-y_1 = m(x-x_1) where m is the gradient and (x_1,y_1) is a point on the line. Since we have two points, we ...
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Answered by Murray M. • Maths tutor
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Edexcel January 2007 - Question 4 (Rates and Differential Equations)

Rates and differential equations is a topic many students find difficult, especially when solving the differential equation is combined with techniques from other topics on the C4 syllabus. I hope my walkthr...
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Answered by Oliver V. • Maths tutor
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