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Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
Why does taking the derivative of a function give you the slope of the tangent?
Why: Because that's what the derivative means, the way it is defined - the slope of the curve at any point of the line.
What does the slope graph tells?
The rate of change on that line. This is called the tangent and is used in the application of the derivative.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
How do you find the slope of a tangent?
Take the derivative of the function.
Can you have a slope of 0?
Yes. Slope = rise/run (or in calculus, the derivative, often denoted dy/dx). A slope of zero indicates there is no rise, i.e., a horizontal line (or in the case of a curve, the tangent line at a given point is horizontal).
What does the derivative at a point mean?
The derivative at any point in a curve is equal to the slope of the line tangent to the curve at that point. Doing it in terms of the actual expression of the curve, find the derivative of the curve, then plug the x-value of the point into the derivative to find the derivative at that point.
How do you find the equation of a tangent line to the graph of fx equals x cubed and x equals -2?
Calculate the derivative of the function.Use the derivative to calculate the slope at the specified point.Calculate the y-coordinate for the point.Use the formula for a line that has a specified slope and passes through a specified point.
How can you write the equation of the tangent line to the curve?
Well if you have found the derivative (slope of the tangent line) of the curve at that point and you know the xy coordinates for that point in the curve then you set it up in y=mx+b format where y is your y-coordinate, x is your x-coordinate and m is your derivative and solve for b
What is the slope of a curve line?
The slope of a curved line changes as you go along the curve and so you may have a different slope at each point. Any any particular point, the slope of the curve is the slope of the straight line which is tangent to the curve at that point. If you know differential calculus, the slope of a curved line at a point is the value of the first derivative of the equation of the curve at that point. (Actually, even if you don't know differential calculus, the slope is still the value of the function's first derivative at that point.)
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.
Find the slope of a tangent line to the graph?
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.
