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The first part of this question requires be student to realise that touching the x axis equates to f(x) equalling 0, so we must equate the expression to 0.

Next we need to factorise the expression....

First I would ask what have they tried, and see if any of their attempts are on the right track - and then guide them from there, if not: 3^x is quite a difficult form to deal with, so is there any other ...

Say that we have a differentiated equation f'(x), and we want to find the orginal equation f(x) from this. We would have to use integration, as differentiation and integration are the reverse of each othe...

X² -> 2X

3X -> 3

7 -> 0

Therefore X² + 3X + 7 integrates to 2X + 3

Use quotient rule to differentiate:

dy/dx = (18x(3x+2) - 3(9x²+1))/(3x+2)²

set dy/dx=0:

54x² + 36x - 27x² - 3 = 0

9x² + 1...