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A curve has the equation, 6x^2 +3xy−y^2 +6=0 and passes through the point A (-5, 10). Find the equation of the normal to the curve at A.

Use implicit differentiation on original equation- 12x + 3x(dy/dx) + 3y - 2y(dy/dx) = 0 dy/dx= -12x -3y/(3x-2y) at A, x= -5 and y= 10 therefore, dy/dx=-6/7 To find the normal of the curve, use the negative r...
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Answered by Chantal G. • Maths tutor
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A curve has the equation y = (x^2 - 5)e^(x^2). Find the x-coordinates of the stationary points of the curve.

This requires the chain rule and the product rule to be used to differentiate the function. The substitution u = x 2 can be used to make this easier. Using this, du/dx = 2x and y = (u-5)e u . Using the produ...
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Answered by Oliver J. • Maths tutor
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Solve x^2 +11x +30 = 0

This is what we call a quadratic equation. To solve, first we need to factorise this equation into two brackets. (x + _ )(x + _) =0To fill the brackets, we need to find 2 numbers that add to 11 and multiply ...
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Answered by Holly R. • Maths tutor
6091 Views

Find a local minimum of the function f(x) = x^3 - 2x.

To find a local minimum (i.e. a point where the function changes from a negative slope into a positive slope), we first need to find all points where the slope of the function is zero. The first derivative o...
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Answered by Karoline H. • Maths tutor
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The equation of line A is (x)^2 + 11x + 12 = y - 4, while the equation of line B is x - 6 = y + 2. Find the co-ordinate(s) of the point at which lines A and B intersect.

While this question may seem complicated, this question is simply asking you to solve the equations of these two lines as simultaneous equations . Line A: x 2 + 11x + 12 = y - 4 --> x 2 + 11x + 16 = y; Li...
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Answered by Ann A. • Maths tutor
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