Prove that the equation y = 3x^4 - 8x^3 - 3 has a turning point at x=2
By definition, turning points occur when the gradient function equals to zero. To prove this we need to differentiate the function given. To differentiate, bring the power down and multiply it by the co-efficient. When we do this we get dy/dx = 12x^3 - 24x^2. Subbing in the value x=2 into this function we get dy/dx = 0. It is important to write a concluding statement with 'prove that' questions. You should write something like ' As the gradient function equals zero at x=2, a turning point must occur here as the gradient is zero' in order to obtain full marks.
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