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A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.

A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x²-6x. We can substitute x = 2 into this equation to give 0 (alternatively solve ...

Answered by Tom C. • Further Mathematics tutor

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Define what degenerate genetic coding means and why it is advantageous

Degenerate genetic coding means that although there are 64 different codons, there are only 21 amino acids, meaning that there are multiple codons which code for one single amino acid. The advantage for t...

Answered by Avinash S. • Biology tutor

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Given y=arctan(3e^2x). Show dy/dx= 3/(5cosh(2x) + 4sinh(2x))

As we cannot immediately differentiate inverse tan we take tan of both sides giving us tan(y)=3e^2x.We then differentiate with respect to x, however this must be done using implicit differentia...

Answered by Matt S. • Further Mathematics tutor

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What are Type I and Type II errors?

A Type I error is when the null hypothesis is incorrectly rejected. The null hypothesis states that there is no relation between the independent variable and the dependent variable. This means the experim...

Answered by Gemma B. • Psychology tutor

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Sketch the curve y = (2x-1)/(x+1) stating the equations of any asymptotes and coordinates of the intersection with the axis. As an extension, what standard transformations from C1 could you use on y=1/x to get this curve?

A good way to start with any of these questions is to guess what type of curve this is, and if that is too difficult then the next best thing is to find some points. In this case it is obvious that it is ...

Answered by Alex D. • Maths tutor

3674 Views