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We know -x^2 has a maximum point of 0 at x=0, and -x^2 dominates the behaviour of f. We complete the square on this eqn, so we have f(x) = -(x - 4)^2 + 16 + c. We note that g(x) = -(x - 4)^2 has a maximum...

a) 27 is higher than the mean. So we can simply calculate the z value. z = (27 - 20)/6 ≈ 1.17. Using the table in the formula booklet, we find that P(Z < 1.17) = 0.8790, so P(X ...

When trying to find stationary points, the first thing you should think about is differentiating. At a stationary point, the gradient of a curve or function is equal to zero. Therefore if we differentiate...

You have to differentiate the equation y=x^2(1+4x)^0.5 with respect to x to get dy/dx and thereby prove the result in the question. An equation composed of the product of two x terms can be differentiated...

Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)