If A(x) is the area under the graph of a nonnegative continuous function f over an interval [a, x], then A'(x) = f (x).Select one:TrueFalse

How do you determine where f is increasing or decreasing?If f  ′(x) 0 on an interval, then f is increasing on that interval.If f  ′(x) 0 on an interval, then f is decreasing on that interval.

Define a function A byA(x) =∫ x1√t dtfor x ≥ 1.i Draw a diagram that indicates the meaning of A(x).ii. What does the Fundamental Theorem of Calculus say about thefunction A?iii. What is A′(4)?

Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time.Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time.In the light of given statements, choose the correct answer from the options given below.JEE Main 2023 (08 Apr Shift 2)ABoth Statement I and Statement II are trueBBoth Statement I and Statement II are falseCStatement I is correct but Statement II is falseDStatement I is incorrect but Statement II is true

Question 13:The graph of g' is shown here. Which of the following statements is (are) true of g?I. g is continuous at x = aII. g is differentiable at x = aIII. g is increasing in an interval containing x = a(A) I only(B) III only(C) I and III only(D) II and III only(E) I, II, and III

Regarding continuous probability functions, the area under the graph represents the ________.