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First, we find the derivative of h: dh/dt= 4-4t. To find the point(s) of interest, we solve dh/dt=0. This gives the answer t=1. In order to determine whether t=1 is a minimum point or maximum point we fin...

When integrating a function which can be defined as a combination of two functions, it can be difficult to tell whether or not to use by parts. We can spot when to use by parts if we look at the composite...

The point of using a substitution when dealing with integrals is to reduce the problem from a very complicated integral to a simplistic one. How can we achieve this with our integral? Well, we know that w...

The factor theorem states that if (x+a) is a factor of f(x), then f(-a)=0. This basically means that if (x+a) is a factor of f(x), then when (x+a)=0, f(x)=0, i.e. when x=-a, f(-a)=0. Our (x+a) in this cas...

The points where the lines cross are the points where the two equations equal each other. To do this we solve simultaneous equations. Call equations as follows:(a) 3x - y = 4(b) x² + 7y = 5 Fir...