The slope of a line and the tangent of the angle between the positive x-axis and the line are related because the tangent of the angle is defined as the ratio of the y-coordinate and the x-coordinate of some point on the line.
Take the derivative of the function.
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.
Ofcourse it is. A tangent (usually known as the tanX f(x)) is the best example.
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 slope of a tangent to the curve of a velocity-time graph represents the acceleration of an object at that specific instant in time. A steeper slope indicates a greater acceleration, while a flatter slope indicates a smaller acceleration.
When you differentiate a function, you find the slope of the function. The slope is also known as the tangent. The slope of a line, given one point, and a second point relative to the first point, but with x different, is given as delta y over delta x. Differentiation is simply taking the limit of the slope, i.e. where delta x approaches zero.
Why: Because that's what the derivative means, the way it is defined - the slope of the curve at any point of the line.
Yes, the derivative of an equation is the slope of a line tangent to the graph.
You find the tangent to the curve at the point of interest and then find the slope of the tangent.
Take a tangent at the point where you want the slope. Then the slope of the graph at that point is the slope of the tangent, which is found by taking another point on the tangent and then taking the change in y between the two points and divid it by the change in x.
The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
The first thing you may want to do would be to find the tangent line to the function. The tangent line is a line that passes through a given point on a function, but does not touch any other point on the function (assuming the function is one to one). Assuming you have the tangent line, the normal line is simply perpendicular to the tangent line- it forms a 90 degree angle with the tangent line. One you have the tangent line and the point which it passes through, you can find the normal line. To obtain the perpendicular line to any function, take the inverse reciprocal of the slope (if your slope was 2, it is now -.5). After that, plug in your (x, y) coordinate, and you can solve for the constant b (assuming there is one). This should give the normal line to a tangent of at a point on a function.