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Debaa
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Is the derivative of a function everywhere the same on a given curve? Or is it just for a infinitesimally small part of the curve? Thank you for the answer.
Yes, you are right. f'(x) = 2x for any value of x.Debaa said:Well f(x) = x^2 is vertically asymptotic. And it's derivative is always 2x isn't it? Will it be 2x everywhere? (I am new to calculus so pls bare.)
Not sure what you mean by this. The graph of y = x2 does not have a vertical asymptote, although as x gets larger (or more negative) the y value gets larger.Debaa said:Well f(x) = x^2 is vertically asymptotic.
Debaa said:And it's derivative is always 2x isn't it? Will it be 2x everywhere? (I am new to calculus so pls bare.)
The derivative of a function is a measure of how the function changes at a specific point. It represents the slope of the tangent line to the curve at that point.
No, the derivative of a function can vary at different points on a curve. It depends on the slope of the tangent line at each specific point.
Yes, the derivative of a function can be negative if the slope of the tangent line at that point is downward, indicating a decrease in the function's value.
The derivative of a function can be found using the derivative rules, such as the power rule or the product rule. It involves finding the limit of the slope of the secant line as the two points on the curve get closer together.
The derivative is important in calculus because it helps us understand how a function changes at a specific point, which is crucial in many real-world applications. It is also used to find the maximum and minimum values of a function, and to solve optimization problems.