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You can rearrange the equation to get 2cos^2(x)+2sin^2(x) = 2. This can be factorised to get cos^2(x) + sin^2(x) = 1 which is a known identity. We can use the fact that 2cos^2(x) = 2sin^2(x) - 2 and subst...

The answer is in the same image as the question.

The first thing we try to do is factorise the numerator and denominator. Let's start with the numerator. We can take a 7 out of the bracket to leave us with 7( x² + 2x ) on the numerator. But w...

dy/dx = 2x + 3dy/dx = 0 at stationary pointTherefore 2x + 3 = 0so x = -3/2so y = (-3/2)^2 +3 (-3/2) + 4so y = 9/4 - 9/2 + 4therefore y = 7/4so the coordinates of the stationary point are (-3/2 , 7/4)

This can seem quite tricky at first, so let's break it down into steps. If we draw a table of x values (for example 0, 1, 2, 3, 4), we can put each value into our equation and find a correspondin...