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dy/dx = 2x - 2 -12x^-1/2dy/dx = 02x - 2 - 12x^-1/2 = 0x = 4 (stationary point)d²y/dx²= 2 + 6x^-3/2when x=4, d²y/dx²= 11/411/4 >...

Student will need to understand that the turning point will be a minimum as the curve is positiveStudent should complete the square:1) factorise out the 2: 2(x² + 7/2 x) - 82) complete the squa...

The second derivative is just two derivatives carried out back to back. In this case we just have to differentiate this function once, and then differentiate the result. The derivative of 2e^(2x) can then...

Logarithms, written in the form log_xy, are another type of mathematical 'operation', just like addition or multiplication. Subtraction as the opposite of addition, division is the opposite of m...

There are two essential tricks to grasp in this question. Firstly, since the equation has only one solution, the Discriminant that will be required would equal 0. Secondly, since we are given f(x) = 2 we ...