# How do you find the points on the parabola #y = 6 - x^2# that are closest to the point (0,3)?

Substitute the equation of the parabola into the distance formula to get the square root of a quartic to minimise. This is quadratic in

As a bonus, we have also calculated the minimum distance as:

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To find the points on the parabola ( y = 6 - x^2 ) that are closest to the point ( (0,3) ), you need to minimize the distance between the given point and any point on the parabola. This can be achieved by minimizing the square of the distance between the points. Therefore, you need to minimize the square of the distance function ( d(x) = (x - 0)^2 + (6 - x^2 - 3)^2 ). To do this, find the critical points of ( d(x) ) by setting its derivative equal to zero and then determine which critical points correspond to the minimum distance.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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