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Solve the simultaneous equation x+y=11(1), x^2+y^2=61 (2)

Make x the subject in the equation x+y=11(1). This will help us eliminate x in the second equation (2).x=11-y (3)Substitute (3) into (2)(11-y) 2 +y 2 =61Expanding the brackets and simplifying gives 2y 2 -22y...
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How do I identify that the coordinate (2,3) is the maximum point of the curve f(x)?

Start by finding the first derivative of the function - by differentiating f(x) with respect to x. Then substitute the x-coordinate, in this case 2, into the first derivative and it will equal zero if (2,3) ...
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What is differentiation and what can it tell me?

Differentiation is something you can do to a function, to tell you about the gradient of the function. For your simple linear, quadratic, cubic, etc. equations, the process is the same every single time. You...
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Answered by Oliver P. • Maths tutor
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Given that y = (3x^4 + x)^5, find dy/dx using the chain rule.

Let u = 3 x 4 + x du/dx = 12x 3 + 1 y = u 5 dy/du = 5u 4 Using the chain rule, dy/dx = dy/du x du/dx = 5 u 4 (12x 3 + 1) dy/dx = 5(3x 4 + x)(12x 3 +1)
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Given that f(x)= (4/x) - 3x + 2 find i) f'(x) and ii) f''(1/2)

This question is asking us to find the first order derivative of f(x) with respect to x, then the second order derivative when x=1/2i) Firstly, let's consider (d/dx)4/x:There are two ways to think about diff...
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Answered by Verity B. • Maths tutor
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