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first we find the first derivative of the function. Here dy/dx = x^2-8x+12. We set this to zero and factorise to obtain the roots of the function. Such that dy/dx = (x-6)(x-2)= 0. This gives the stationar...

As both equations have y on the left hand side we can put the right hand sides equal to each other, so 2x=x+3. We can then subtract x from both sides. This gives 2x-x on the left hand side which is x, and...

Looking at this question the first thing we should notice is that there is a an x squared inside a bracket which is also squared. As there is function inside a function we must use the chain rule. The sim...

Looking at this equation you can see that it is in the form of y = mx + c and we know that this is the equation of a straight line. One way to solve this would be to inspect the equation and see that the ...

Notice that integration is simply the opposite of differentiation. So, if we just integrate this term-by-term then we can find an expression of y in terms of x.

So, when we integrate dy/dx becomes ...