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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.
CH
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 ...
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Answered by Vithya N. • Maths tutor
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Explain three difficulties economists face when they try to measure unemployment accurately.

Unemployment, while useful in some cases, is inherently flawed as a metric for socio-economic progress. Official unemployment statistics fail to take into account the issue of hidden unemployment, defined as...
CR
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What is the difference between London dispersion forces and hydrogen bonds?

Both are a type of inter molecular forces which means they act between more than 1 molecules. Do not confuse them with intra molecular forces acting within 1 molecule. London dispersion forces act between al...
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Answered by Daria S. • Chemistry tutor
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Find all real solutions of (x^2 +4x +3)^(x^2 -6x+8) = 1

Rewrite as a^b = 1, where a = x^2+4x+3 and b = x^2-6x+8List the cases for which a^b = 1Case 1: a = 1:So x^2+4x+3=1 => x^2+4x+2=0 => x=-2 +/- sqrt(2)Case 2: b=0, a ≠ 0:b=(x-4)(x-2) => x = 2, x=4Check...
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Answered by Nicholas M. • PAT tutor
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