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Solve the simultaneous equations xy=2 and y=3x+5.

x=1/3 and y=6 or x=-2 and y=-1
SS
3123 Views

Given f(x)= 8 − x^2, solve f(3x) = -28

First substitute (3x) into the equation for f(x), giving f(3x) = 8 - 9x 2 . This is then equal to -28 and so it is remains to solve the equation 8 - 9x 2 = -28. This can be written as 9x 2 = 36, dividing thr...
GG
4136 Views

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
3471 Views

A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.

The gradient of the tangent at P (=1) will be equal to the gradient of the curve at point P (=1). The gradient at a point on a curve is given by dy/dx (the differential). First, differentiate the equation of...
ST
3114 Views

Find and describe the stationary points of the curve y = x^2 + 2x - 8

Stationary points occur when the derivative is = 0Derivative: 2x + 2 = 0, so a stationary point occurs when x = -1y = 1 + 2 - 8 = -5Second derivative = 2Therefore, the stationary point (-1,2) is a minimum
MN
2479 Views