How do I tell if a curve has a maximum or a minimum?
Firstly we need to find the stationary point on the curve. We know what at a stationary point the gradient is zero so we will find the gradient of the curve. We do this by differentiation, when we have differentiated the curve we can set the result equal to zero to find the place where the gradient is zero. We will then have our stationary point or points. Now we need to find out if this point is a maxima or a minima. We do this by differentiating the gradient, so differentiating the equation of the curve twice. Then sub into this equation the the coordinates of the stationary point. If the answer is negative the point is a maxima, if the answer is positive the point is a minima.
CK
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