Find the coordinates of the critical point of the function below and state whether it is a maximum or a minimum point. Give your answers to $2$ decimal places where necessary.
\n$F(x)=\\simplify {{f}x^2+{g}x+{h}}$
\nFirstly, find the first and second derivatives:
\n$F'(x)=$ [[2]]
\n$F''(x)=$ [[3]]
\n\nSecondly, find $x$ such that $F'(x)=0$
\ncritical point $=$ [[0]]
\nvalue of $F$ at the critical point $=$ [[1]]
\nThe critical point is a point of [[4]]
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\nHere, the question takes you throught the stages needed to find the solution. The reason we differentiate is that the derivative of a function tells us its gradient at a given point, and we want to find where the function has gradient zero because when the gradient is zero we either have a maximum or a minimum point.
\nPart C
\nThe first part of this question is similar to parts A and B. The tricky bit is the second part! You need to work out the value of $t$ that produces the maximum piont but that is not the final answer - you need to use that value of $t$ to find the maximum height, which you do by substituting $t$ into the original function to find $y$.
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