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The curve C has equation y = 3x^4 – 8x^3 – 3 Find (i) dy/dx (ii) the co-ordinates of the stationary point(s)

i) dy/dx=12x^3-24x^2ii) the stationary points occur when dy/dx = 0 so we must find the solutions to 12x^3-24x^2=0.12x^3-24x^2= 12x^2(x-2)=0Therefore our stationary points are when 12x^2=0 ie x=0 and x-2=0 ie...
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Integrate xlnx with respect to x

1/2 *x 2 *lnx -1/4x 2 +C
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Answered by Matilda P. • Maths tutor
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What is the binomial distribution and when should I use it?

In statistics, we use the binomial distribution to model situations when we take an experiment (like rolling a die) and we repeat that experiment a certain number of times. Importantly, within each experimen...
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Answered by Taylor E. • Maths tutor
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A new car costs £12,000. It decreases in value by 5% each year for the first 5 years and then increases in value by 2% after that. How much does it cost after 7 years?

12,000 x 0.95^5=9285.37 7-5=2 9285.37x1.02^2=9660.50
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Answered by Matilda P. • Maths tutor
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Differentate sin(x^2+1) with respect to x

y = sin(x 2 +1) In general, the chain rule is: dy/dx = f(g(x)) = df/dg * dg/dx Applying this to y: dy/dx = d(sin(x 2 +1))/d(x 2 +1) * d(x 2 +1)/dx = cos(x 2 +1) * (2x) = 2xcos(x 2 +1)
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