x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
You find the gradient of the curve using differentiation. The answer is 0.07111... (repeating).
x2 / y = (6)2 /2 = 36/2 = 18
y = x - 4/x so gradient = dy/dx = 1 + 4/x2 When y = 3, x - 4/x = 3 x2 - 3x - 4 = 0 so x = -1 or x = 4 When x = -1, gradient = 1 + 4/(-1)2 = 1 + 4/1 = 1+4 = 5 When x = 4, gradient = 1 + 4/(4)2 = 1 + 4/16 = 1+1/4 = 1.25
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
Gradient to the curve at any point is the derivative of y = x2 So the gradient is d/dx of x2 = 2x. When x = 2, 2x = 4 so the gradient of the tangent at x = 2 is 4.
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
Gradient = 2
Gradient = 2
You find the gradient of the curve using differentiation. The answer is 0.07111... (repeating).
x2 / y = (6)2 /2 = 36/2 = 18
y = x - 4/x so gradient = dy/dx = 1 + 4/x2 When y = 3, x - 4/x = 3 x2 - 3x - 4 = 0 so x = -1 or x = 4 When x = -1, gradient = 1 + 4/(-1)2 = 1 + 4/1 = 1+4 = 5 When x = 4, gradient = 1 + 4/(4)2 = 1 + 4/16 = 1+1/4 = 1.25
y=2 + 3x seems like a linear equation, therefore, y=3x + 2.The gradient is 3.
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
Gradient = -2 y-intercept = -4
2
-2