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f(x)=12x^2e^2x - 14, find the x-coordinates of the turning points.

f(x)=(12x^2)(e^2x) - 14, so using the chain rule f'(x)=(24x)(e^2x) + (12x^2)(2e^2x).To find the turning points set f'(x)=0, so (24x)(e^2x) + (24x^2)(e^2x) = 0. Thus (24xe^2x)(1+x)=0. Thus x=0 or x=-1.
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Answered by Charlotte H. • Maths tutor
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Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y - x = 1

Let's label the equations x 2 + y 2 = 25 (1) y - x = 1 (2). We can use substitution to solve this simultaneous equation. Let's make y the subject of the equation (2) and we get y = x + 1. Now, lets find y 2 ...
VN
Answered by Vithya N. • Maths tutor
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Rationalise the surd: 2/root(x)

To rationalise a surd means to manipulate a fraction involving terms which are being square rooted so that no term in the denominator is being square rooted. For this example 2/root(x) we multiply the fracti...
DT
Answered by Daniel T. • Maths tutor
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Solve 3x^2+7x-13=7 to find x.

Firstly, you need to get the equation to equal zero, so that you can use the quadratic formula to solve. Therefore you subtract 7 from both sides, meaning the equation becomes: 3x^2+7x-20=0. Recall the quadr...
EM
Answered by Ellie M. • Maths tutor
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Solve (6x-2)/4 - (3x+3)/3 = (1-x)/3. (4 marks)

(6x-2)/4 - (3x+3)/3 = (1-x)/3 multiply both sides of the equation by 12=lowest common multiple of 4 and 3 3(6x-2) - 4(3x+3) = 4(1-x) expand brackets 18x - 6 -12x - 12 = 4 - 4x simplify 6x - 18 = 4 - 4x10x = ...
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Answered by Eleanor L. • Maths tutor
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