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What is the slope of a line parallel to the line whose equation is Y equals 2 over 5X-3?
The line described by the equation is a hyperbola and its gradient is different along its length. Its gradient is -10/(5x-3)2 except where x = 3/5 and the curve is not defined. The general form of a parallel curve is y = a + 2/[5(x + b) - 3] where a and b are constants.
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
How want to know that the gradient of a curve in displacement-time graph is increasing or decreasing?
If the gradient is a positive number the curve is increasing, and if the gradient is a negative number it is decreasing.
What is the gradient of a sine curve?
Cosine
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
What is the gradient of the tangent to the curve at x equals 2 if Y equals x2?
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.
What is the slope of a line parallel to the line whose equation is Y equals 2 over 5X-3?
The line described by the equation is a hyperbola and its gradient is different along its length. Its gradient is -10/(5x-3)2 except where x = 3/5 and the curve is not defined. The general form of a parallel curve is y = a + 2/[5(x + b) - 3] where a and b are constants.
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
What is the equation to the tangent line to the curve xy plus y2 equals 0 at the point x equals 3 and y equals 0?
y=0. note. this is a very strange "curve". If y=0 then any value of x satisfies the equation, leading to a curve straight along the y axis. For any non-zero value of y the curve simplifies to y = -x. The curve is not differentiable at the origin.
How want to know that the gradient of a curve in displacement-time graph is increasing or decreasing?
If the gradient is a positive number the curve is increasing, and if the gradient is a negative number it is decreasing.
The derivative finds the of a curve?
The gradient of the tangents to the curve.
How can you tell whether the gradient of a curve is increasing or decreasing?
Differentiate the curve twice and then enter a value for x. If the answer is positive, the gradient is increasing at that point. If the answer is negative, the gradient is decreasing at that point. And if the answer is zero, the gradient is not changing.
What is the gradient of a sine curve?
Cosine
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
The curve with equation y2 equals x3 plus 3x2 is called the Tschirnhausen cubic?
y2=x3+3x2
How do you find the value of c when the straight line y equals x plus c touches the curve y equals 3 -x -5x squared?
-2
