how do you calculate the instantaneous rate of change. is that the derivative.
also:
if f is the antiderivate of
(x^2)/(1+x^5 such that f(1)=o then
f(4)=?
How would i find the integral of that? i don't even know what the first step is to get the answer. also, on this question, i can use the calculator but i don't what number i would need.
The answer choices are:
-0.012,0,.016,.376,0629. I'm thinking it's zero but i have no idea.
yes, instantaneous rate of change is the first derivative.
The second question can be integrated with the calculator here:
http://integrals.wolfram.com/index.jsp
Note the constant of integration does not appear, you have to solve for that with f(1)
To calculate the instantaneous rate of change of a function at a given point, you would indeed take the derivative of the function at that point. The derivative can be thought of as the rate at which the function is changing at any given point.
Regarding the second question about finding the integral of the function:
The function you provided is (x^2)/(1+x^5). To find the antiderivative or integral of this function, we can use techniques of integration. Since the integral involves the variable "x," you need to find an antiderivative, which is essentially the reverse process of differentiation.
To find the integral of this function, you can use the calculator provided at http://integrals.wolfram.com/index.jsp. Simply enter the function (x^2)/(1+x^5) and click "Evaluate." The calculator will compute the integral for you.
However, the provided function is missing a closing parenthesis. Assuming that the function is (x^2)/(1+x^5), you can substitute it into the calculator and click "Evaluate."
Once you have the value of the integral, you can use the condition f(1) = 0 to determine the constant of integration. Evaluate the integral at x = 1 and equate it to 0: f(1) = 0. This will allow you to solve for the unknown constant.
After determining the value of the constant of integration using the condition f(1) = 0, substitute x = 4 into the antiderivative (or integral) to find f(4). The calculator will help you evaluate this expression.
Looking at the answer choices (-0.012, 0, 0.016, 0.376, 0.629), the answer will depend on the value of the constant of integration that you solve for. Without knowing the specific value of the constant, it is difficult to determine the exact value of f(4). Therefore, more information is needed to accurately select the answer choice.