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Consider the functions f(x) = −x^3 + 2x^2 + 3x and g(x) = −x^3 + 3x^2 − x + 3. (a) Find df/dx (x) and hence show that f(x) has turning points at when x = 2 /3 ± √ 13/ 3 . [5] (b) Find the points where f(x) and g(x) intersect. [4]

a) First differentiate f(x) using standard polynomial derivative rules which gives, df/dx=-3x^2+4x+3. The derivative function gives the gradient of f for any value of x. Turning points occur when the gradien...
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Assess the economic effects of a depreciation on a countries currency

Depreciation involves reducing the value of the nations currency against others. Under a managed float this could be achieved by a central bank selling its own currency in exchange for foreign currency. This...
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Answered by Oliver B. • Economics tutor
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Solve the following: sinx - cosx = 0 for 0≤x≤360

We know that sinx/cosx = tanx. Therefore we can write sinx - cosx = 0 as sinx = cosx . By diving both sides by cosx, we get tanx = 1. By taking tan inverse of both sides, we can see that for 0≤x≤360, we get ...
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Answered by Aaman K. • Maths tutor
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State and explain all of the factors which can shift the demand curve of a product

The Quantity Demanded of a product is the quantity of a good or service that consumers are willing and able to buy at different prices in a specified time period. The Demand curve is a curve which shows the ...
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Answered by Oliver B. • Economics tutor
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Solve the following quadratic equation for X: X^2 -10X + 24=0

We can factorise the quadratic equation by noting that two numbers which multiply to get 24 and that add to get -10 are: -6 and -4. Therefore, we get (X-6)(X-4)=0 and we can solve for X to get X = 6 or X = 4.
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Answered by Aaman K. • Maths tutor
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