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You find the tangent to the curve at the point of interest and then find the slope of the tangent.
You find the slope of the tangent to the curve at the point of interest.
Tangent is used in calculus to compute the slope of a curve. Because curves do not have uniform slopes, unlike lines, their slopes change. A tangent is the slope of a curve at a specific point.
The slope of the tangent line at the maximum point of the curve is zero. So we say that as a curve point approaches to the maximum point, the slope of the tangent line at that point approaches to zero.
By differentiating the answer and plugging in the x value along the curve, you are finding the exact slope of the curve at that point. In effect, this would be the slope of the tangent line, as a tangent line only intersects another at one point. To find the equation of a tangent line to a curve, use the point slope form (y-y1)=m(x-x1), m being the slope. Use the differential to find the slope and use the point on the curve to plug in for (x1, y1).
Slope of a Curve A number which is used to indicate the steepness of a curve at a particular point.The slope of a curve at a point is defined to be the slope of the tangent line. Thus the slope of a curve at a point is found using the derivative
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.
You're familiar with the xy-plane. A line with negative slope is one that goes down toward the right. A curve has a negative slope at a point if the tangent line to the curve at that point has a negative slope.
Slope = (vertical change)/(horizontal change), commonly referred to as rise/run. If the graph is a straight line, then you can count squares or measure how much change in vertical, over a specified change in horizontal. If it is a curve, then you need to have a tangent line (a line that touches the curve at a specific point and has the same slope as the line), then you can determine the slope of that line using the method described, above.
1) Find time = 10 s on the curve. 2) Draw a line tangent to the point time = 10 s on the curve. 3) Use two points on the tangent line to find the slope of the line. 4) The slope of the line is the instantaneous rate in M/s.
instantaneous
the slope of a tangent to the curve of a V vs T graph is acceleration at that point in time. the derivative of the function for the V vs T graph would be the function for acceleration at any given time