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A curve has equation y = 20x −x^2 −2x^3 . The curve has a stationary point at the point M where x = −2. Find the x-coordinate of the other stationary point of the curve.

dy/dx = 20 - 2x - 6x 2 = -6x 2 - 2x + 20 which factorises to dy/dx = (10 - 6x)(2 + x). This shows that x=-2 and x=10/6=5/3 are stationary points of y = 20x −x 2 −2x 3 .
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Answered by Xixi Y. • Maths tutor
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How to prove that Integral S 1/(a^2+x^2) dx= 1/a arctan(x/a) + C ?

In order to answer this question, at first we need to use the method of substitution. That means, we're trying to replace x with a different variable u. Lets use the substitution of x = a tan u, then du/dx =...
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Answered by Judyta W. • Maths tutor
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Solve the following simultaneous equations: x^2 + 2y = 9, and y = x + 3.

Label the two equations as the following: x 2 + 2y = 9 y = x + 3 Equation 2 can be substituted into equation 1, giving: x 2 + 2( x + 3 ) = 9Expanding the brackets and subtracting 9 from both sides means equa...
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Answered by Ximena B. • Maths tutor
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How do I solve simultaneous equations by substitution?

You can solve simultaneous equations by either substitution or elimination. Say we have the equations:(1) 8y + 6x = 24 and (2) 2y - x = 6SUBSTITUTION METHODFirst, you need to find x in terms of y (or y in te...
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Answered by Joshua N. • Maths tutor
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Find all values of x in the interval 0 ≤ x ≤ 2pi for 2sin(x)tan(x)=3

This questions involves the use of trigonometric identities, specifically [1] tan(x) = sin(x)/cos(x) and [2] sin 2 (x) + cos 2 (x) = 1. Start by rearranging the given equations to tan(x) = 3/2sin(x) by divin...
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Answered by Jasmin C. • Maths tutor
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