Find the turning points and their nature of the graph y = x^3/3 - 7x^2/2 + 12x + 4
Answer = (3,17.5) maximum (4,17.33) minimum
First differentiate y = x^3/3 - 7x^2/2 + 12x + 4 to find dy/dx. Now, at turning points dy/dx = 0 and factorise to find x when dy/dx = 0. Put x back into orginal equation to find y at turning point.
Now to find the nature of the turning point take your equation for dy/dx and differentiate again to find d^2y/dx^2. Put x of both points into this equation. If equation comes out positive the turning point is a minimum. If it comes out negative turning point is maximum. Now plot these points on a graph and see how they add up
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