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The question has given us a function and wants us to determine whether or not any maximums/minimums exist (and if so identify then). We know maximums/minimums occur when the derivative of the equation is ...

Don't forget, in order to find the area under a curve y=f(x) between two values x=a and x=b we integrate f(x) between a and b.Thus to find the area enclosed between two curves y=f(x) and y=g(x) we simply ...

We can take logs of both sides straight away, and using the log rule that alogb = log(b^a)So(4x-1) log(2) = (5 - 2x) log(3)We can expand the bracketsso (4x)log(2) - log(2) = 5log(3) - 2xlog(3)We can group...

Firstly we need to expand out y into a series of terms to make it easier for us to compute the derivative . You multiply out the brackets to get y=(x³-3x²+4x-12)/2x then we divide ea...

z* is the complex conjugate of z therefore z* = x - yi. So 16 + 32i = 5(x + yi)-3(x - yi), real: 16 = 5x - 3x => 16=2x => x=8, imaginary: 32 = 5y + 3y => 32 = 8y => y=4, therefore z = 8 + 4i.<...