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Firstly, recognise the relevant equations. The two functions are y = mx and y = ln(x). As the straight line is a tangent, we know that at a certain point x₀, the functions and ...

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Water has a very high specific heat capacity due to the collective forces of the many hydrogen bonds. A lot of energy goes into breaking these bonds rather than raising the temperature of the water, hence...

No, and we may take a counterexample to see why. If y=x^5+5/3x^4, dy/dx=5x^4+20/3x^3, d2y/dx2=20x^3+20x*2=20x^2(x+1). Setting this to 0 will give us the candidates for a POI, but not all these numbers wil...

The period between childhood and adulthood is a time of great transition and turbulence with regards to changing bodies, close relationships, and expectations. It is one of the most rapid phases of develo...