Give an example of a (discontinuous) function that does not satisfy the conclusion of the IVT on [-1, 1]. Then show that the func- tion 1 sin - x+0 f(x)= x = 0 satisfies the conclusion of the IVT on every interval [-a,a].

Q: Show that the function is harmonic and analytic w=3Z² + 4iZ

A:

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Determine whether f(x)=sinx+cosx is an odd or even number

A: Given function is f(x)=sinx+ cosx

Q: Find the absolute max. and min. of each function y=√4−x^2, (−2,1)

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Plot the graphs of f(x) = x(x - 3) (x + 3) and g(x) = cos 2 x together on the same set of axes and…

A: In the question it is asked to draw diagram for f(x)=x(x-3)(x+3). Also it is asked to draw…

Q: (max, argmax, min, argmin) Let f(x) := (2+ sin(27x)) and A := [0, 2]. Compute: max,A f(x) and argmax…

A:

Q: Q3\ a) Find the values of a and b to make the functions continuous at every x: ax + 2b 2) g(x) = }x²…

A: Given function is,  f(x)=-2        ;x≤-1ax-b   ;-1≤x≤13          ;x>1