Consider the cubic graph shown. What are the coordinates of the local maximum?
Well, if we consider what local maxima or minima are, well, if we’re at a maximum or minimum point, the tangents at these points have a slope, or gradient, of zero. So therefore, it means that the tangents must be horizontal lines. Well, therefore, we can notice that on our graph, we have two such points. And I’ve marked them in orange and pink.
And in orange, we have the local maximum cause that’s the highest output out of the two. And in pink, we have the local minimum. And we can see that because if we look logically, one would be at the bottom and one would be at the top, so maximum, minimum. So therefore, the coordinates of our local maximum are going to be negative two, three.