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find the stationary point of the curve for the equation y=x^2 + 3x + 4

dy/dx = 2x +32x + 3 = 0x= 3/2(3/2) 2 + 3(3/2) + 4 = 2.25 + 4.5 + 4 = 10.75
IH
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A straight line passes through the point (0, 6) and is perpendicular to y = 4x - 5. Find the equation of this line, giving your answer in the form y = mx + c .

perpendicular so the gradient is -1/4 y= -1/4x +CSub in the coordinate (0,6) 6 = -1/4 (0) +C C=6y=-1/4x +6
MS
Answered by Maria S. • Maths tutor
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Explain what is meant by allocative efficiency and Pareto optimality. Consider whether they are linked .

Allocative efficiency refers to when the bundle of goods being produced is an efficient bundle. Hence, if allocative efficiency is not being achieved then resources can be reallocated to produce a different ...
TD
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factorise x^2 - 8x -65

Two numbers add/ subtract to make -8Two numbers multiply to make -65. These are 1 and 65 as well as 5 and 13Seeing as 1 and 65 cant add or subtract to make -8 the numbers we'll use are 5 and 13. These also s...
KC
Answered by Kavi C. • Maths tutor
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The normal to the curve C when x=1 intersects the curve at point P. If C is given by f(x)=2x^2+5x-3, find the coordinates of P

Differentiate C:dy/dx=4x+5When x=1dy/dx=4(1)+5dy/dx=9This is gradient of tangent.Gradient of normal=-1/9When x=1, y=4y-4=-1/9(x-1)y=(-1/9)x+(37/9)(-1/9)x+(37/9)=2x^2+5x-30=2x^2+(46/9)x-(64/9)x=1 or x=-32/9P ...
HC
Answered by Hannah C. • Maths tutor
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