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Prove by contradiction: Assume negation to be true i.e. √2 is rational Then √2 can be written in the form a/b where a and b are integers with no common factor (the fraction cannot be simplified) => a/b...

Differentiate y to get: dy/dx = 7-3x^2 , dy/dx = 0 , therefore x=(+/-)sqrt(7/3) d^2y/dx^2 = 6x , substitute x values in to y=7x-x^3 and d^2y/dx^2 to find coordinates and the type of the stationary point.<...

(x+3)(x-7)

= (xx) + (x-7) + (x3) + (3-7)

= x^2 - 7x + 3x - 21

= x^2 - 4x - 21

Key here is to ensure you multiply each term in one bracket by both in the other...

The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now se...

[use of board] So, Pythagoras' theorem states that a^2+b^2=c^2. Therefore, we need to mark the triangle with a, b &c. a and b do not matter, c must be the longest edge, that creates the diagonal. Put ...