A curve is defined by the equation y = (x + 3)(x – 4). Find the coordinates of the turning point of the curve.

The turning point of a curve is the point at which it will turn, therefore, either the maximum or minimum point. Firstly, you need to expand out the brackets so the equation looks like a standard curve equation. When expanded, the equation will be y = x² – x – 12. The turning point will be when dy/dx is equal to 0.Therefore when the curve equation is differentiated you get 2x - 1 . Set this to 0.When solved, x will equal 0.5 . This is the x coordinate of the turning point. You need to find the y coordinate as well. To do this, fill 0.5 back into the original curve equation where an x is. The equation will now read, y = 0.25 - 0.5 - 12 . Y will equal -12.25 . Therefore the turning point will be at (0.5, -12.25) . You have now finished the question.