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Find the stationary points of the curve y=x^4-8x^2+3 and determine their nature.

First we will differentiate y to find dy/dx= 4x 3 -16x. Stationary points exist at dy/dx=0 so we set 4x 3 -16x=0 and solve for x. x(4x 2 -16)=0. So x=0 or 4x 2 -16=0. If 4x 2 -16=0 then x 2 =4 and so x=2 or ...
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Determine the first derivative of the following curve defined by parametric equations x = 20-5t and y = t^5.

First remember that a parametric curve z = (x(t), y(t)) can be differentiated using the following formula (derived using the chain rule): dz/dt = (dy/dt)/(dx/dt). We should now find dy/dt and dx/dt (which ar...
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Answered by Federico C. • Maths tutor
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I don't fully understand the purpose of integration. Could you please explain it to me?

I have written "… " where I would imagine the student is replying. I have then provided prompts assuming that the student did not come up with the answer straight away. Integration can be useful in...
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Answered by Rebecca L. • Maths tutor
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Differentiate y=(4x^2-1)^3

When differentiating a composite function y = (4x 2 -1) 3 , the chain rule needs to be used. The chain rule is dy/dx= dy/du x du/dx In this instance we need to assign u and y in order to differentiate and ge...
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Find the values of x such that: (log3(81)+log2(32))/(log2(x)) = log2(x) (5 marks)

log 3 (81) = 4 , log 2 (32) = 59/log 2 (x) = log 2 (x)9 = (log 2 (x)) 2 3 = log 2 (x) , -3 = log 2 (x)x = 8 , x = 1/81 mark per line
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Answered by Iver E. • Maths tutor
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