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A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x²-6x. We can substitute x = 2 into this equation to give 0 (alternatively solve ...

To find the gradient of the tangent, we can differentiate to give dy/dx=3x^2+9. We can now put in x=2 to find the gradient at (2,1): 3(2)^2+9=21. Therefore the gradient is 21 at (2,1).

Firstly you should expand the brackets in this situation in order to collect the like terms, so get all the x's on one side and all the constants on the other side of the inequality. Expanding the bracket...