A little reminder to students doing Calculus now

A little reminder to students doing Calculus now

JC Mathematics

When \frac{dy}{dx} = 0 , it implies we have a stationary point.

To determine the nature of the stationary point, we can do either the first derivative test or the second derivative.

The first derivative test:

First Derivative Test

Students should write the actual values of \alpha^-, \alpha, \alpha^+ and \frac{dy}{dx} in the table.

We use this under these two situations:
1. \frac{d^2y}{dx^2} is difficult to solve for, that is, \frac{dy}{dx} is tough to be differentiated
2. \frac{d^2y}{dx^2} = 0

The second derivative test:

Second Derivative Test

Other things students should take note is concavity and drawing of the derivative graph.

Random Questions from 2016 Prelims #4

Random Questions from 2016 Prelims #4

JC Mathematics


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A curve has equation y^2=4x and a line l has equation 2x-y+1=0 as shown above.

B(b, 2\sqrt{b}) is a fixed point on C and A is an arbitrary point on l. State the geometrical relationship between the line segment AB and l is the distance from B to A is the least.

Taking the coordinates of A as (a, 2a+1), find an equation relating a and b for which AB is the least.

Deduce that when AB is the least, (AB)^2 = m (2b - 2\sqrt{b} +1)^2 where m is a constant to be found. Hence or otherwise, find the coordinates of the point on C that is nearest on l.