How do you find the interval where f is increasing and decreasing?

If f′(x) > 0, then f is increasing on the interval, and if f′(x) < 0, then f is decreasing on the interval.

What is the instantaneous rate of change of a function?

The instantaneous rate of change is the rate of change of a function at a certain time. If given the function values before, during, and after the required time, the instantaneous rate of change can be estimated.

What is the definition of the definite integral of a continuous function f x over the interval a/b ]?

Given a function f(x) that is continuous on the interval [a,b] we divide the interval into n subintervals of equal width, Δx , and from each interval choose a point, x∗i x i ∗ . Then the definite integral of f(x) from a to b is. ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx ∫ a b f ( x ) d x = lim n → ∞ ⁡

Why is the integral of zero a constant?

Originally Answered: why is integration of zero a constant? It depends on the type of integral you’re asking about. As an indefinite integral ∫0dx, it is C. This is justified by stating that since there is no range involved, the derivative of a constant = 0, therefore the strict anti-derivative of 0 is any constant.

What is the instantaneous rate of the reaction at T 800 S?

OneClass: What is the instantaneous rate of the reaction at t=800s? The answer is rate= 6.8×10^-5 m/s…

Is instantaneous rate positive or negative?

Most certainly! When the instantaneous rate of change of a function at a given point is negative, it simply means that the function is decreasing at that point. As an example, given a function of the form y=mx+b , when m is positive, the function is increasing, but when m is negative, the function is decreasing.

Is the integral a continuous function?

The integral of f is always continuous. If f is itself continuous then its integral is differentiable. If f is a step function its integral is continuous but not differentiable. A function is Riemann integrable if it is discontinuous only on a set of measure zero.

What is the value of integration of 0?

The integral of 0 is C, because the derivative of C is zero.

Which integral or integrals have a value of zero?

Therefore, the definite integral is always zero.