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Find the turning points on the curve with the equation y=x^4-12x^2

y = x^4 - 12x^2 dy/dx = 4x^3 - 24x The turning points are where dy/dx = 0 4x^3 - 24x =0 x(4x^2 - 24) = 0 Therefore one of the turning points is at x = 0 4x^2 - 24 = 0 4x^2 = 24 x^2 = 6 x = +/- √6 Substitute ...
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Solve 7(x+2)=5x+21

The first thing we must realise is that there are brackets in this equation and thus this has to be dealt with. We expand out the brackets on the left side by multiplying 7 by x and 2 to obtain '7x+14'. We n...
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Draw a graph of x = (y+4)/4.

Note: There are multiple ways to do this, so find a way that works for you!Step 1: Get rid of the fraction.Step 2: Rearrange the new formula into y = mx + c.Step 3: Find the y-intercept and the x-intercept.S...
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Answered by Tarin N. • Maths tutor
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How do you solve simultaneous equation where one of them involves powers?

Example: y - 3x = 2 , x 2 + y 2 = 4 y= 3x + 2 x 2 + (3x+2) 2 = 4 10x 2 + 12x + 4 = 4 10x 2 +12x=0 x(10x+12)=0 x=0 or x=-1.2 y=3 0 + 2 = 2 (0,2) is a solution y = 3 -1.2 + 2=-1.6 (-1.2,-1.6) is a solution
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Answered by Luke F. • Maths tutor
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Show that arctan(x)+e^x+x^3=0 has a unique solution.

Since either sketching the function f(x)=arctan(x)+e x +x 3 or evaluating the precise/approximated solutions of the equation would be impossible with A-level techniques, we have to come up with an "alte...
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