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Im kinda stuck on proving that the derivative of a function is always increasing or decreasing e.g. 2x^3-3x^2+5x+1 and [always increasing], -x^3+2x^2-5x+7 [always decreasing]. What is the proper way of concluding why its always positive/negative

How hard can balancing and various questions related to chemical equations get?

What is a good textbook which contains permutations and combinations considering that Cambridge doesn't have that topic?

If we are to prove LHS=RHS can we use the method of LHS-RHS=0 thus proving the fact LHS has to be equal to RHS.

Can anyone derive this equation properly f(x)=(r-6)^3-1/(r-6)^3+1

|x+2|+|3x-1|<5 |x-3|+|x+4|=x-2 thanks ^^

What are the requirements for Extension 2 Mathematics?