PrashntS said:
The motive was to find the tangent.. But I can't seem to find it.. when I plot the graph to this yperbola, I just CANT figure out how to proceed! HELP!
PS: This question was in exams today.. If the question is missing some info, please mention -.-
A tangent is a straight line that touches a curve at only one point, without crossing through it. It represents the instantaneous rate of change or slope of the curve at that specific point.
The derivative is used to find the slope of the tangent line at a specific point on a curve. This slope is then combined with the coordinates of the point to form the equation of the tangent line using the point-slope form.
Yes, the concept of tangents can be applied to other shapes such as circles, ellipses, and parabolas. In these cases, the tangent line will touch the shape at only one point and represent the slope of the curve at that point.
The concept of tangents is used in many real-life applications, including physics, engineering, and economics. For example, in physics, tangents are used to calculate the velocity of an object at a specific moment in time, while in economics, tangents can be used to determine the marginal cost of producing one more unit of a product.
The derivative is the mathematical representation of the slope of a curve at a specific point, while the tangent line represents this slope visually. In other words, the derivative is the general concept and formula, while the tangent is the visual representation of that concept in a specific scenario.
