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jimen113
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Homework Statement
the antiderivative for 5[tex]\sqrt{}x[/tex]
Homework Equations
The Attempt at a Solution
It almost looks like the derivative of the function [tex]\sqrt{}x[/tex]
Yes (to part one)Defennnder said:Do you mean [tex]\int_1^7 \frac{5}{\sqrt{x}} \ dx[/tex]?
If so, then x^(3/2) shouldn't be part of your answer.
A derivative of a function represents the rate of change of that function at a specific point. In other words, it is the slope of the tangent line to the function at that point.
The derivative is important because it helps us understand the behavior and characteristics of a function. It can tell us whether a function is increasing or decreasing, at what rate, and can also help us find maximum and minimum values.
The derivative of a function can be found by using a specific formula or by using rules such as the power rule, product rule, quotient rule, and chain rule. These rules involve taking the derivative of each term in the function and combining them using specific operations.
A derivative and an antiderivative are related but have different meanings. A derivative represents the rate of change of a function at a specific point, while an antiderivative is the reverse process of finding a function whose derivative is equal to the original function.
Yes, the derivative of a function can be negative. This means that the function is decreasing at that point. The sign of the derivative can tell us about the direction of the function's slope at that point.