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y = (x + 2)(x + 5)

steps as follows:x times x = x 2 2 times 5 = 102 times x = 2xx times 5 = 5xthen add these together:y = x 2 + 7x +10x = -2, -5; y = 0, 10
GL
Answered by Georgie L. • Maths tutor
2872 Views

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...
CG
Answered by Chantal G. • Maths tutor
6591 Views

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...
OJ
Answered by Oliver J. • Maths tutor
4438 Views

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 ...
HR
Answered by Holly R. • Maths tutor
5692 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
4380 Views