V * 00 C0 Suppose f"(x) > 0 on some interval (a, b). Check all of the following statements that must be true. f is increasing on the interval (a, b). O f is decreasing on the interval (a, b). O f is decreasing on the interval (a, b). O f is increasing on the interval (a, b). O f is concave upward on the interval (a, b). O f is concave downward on the interval (a, b). arch PrtSc Insert F6 F8 F12 & 80 69 HI

Q: The domain of f is the interval [A, B

A:

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: 72. Is the function given by F(x) continuous on R? x- 5 3.

A: Given function is Fx=3x-5.

Q: 3. Let f be a function from X into Y. Suppose A and B are subsets of X. Prove that f(A U B) = f(A) U…

A:

Q: How many of these injective functions are increasing? (i.e. if a<b then f(a) < f(b).

A:

Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: Find the limit of the function as x approaches 2+.* -5 -4 -3 -2 -1 O 1 DNE Option 5

A: What is the limit of function as x approaches to 2+

Q: Suppose f is a continuous function, and the following facts hold: f(2,10,9) = 8, and Duf(2,10,9) =…

A: Definition: Directional derivative is the rate of change of f(x, y, z) in the direction of the unit…

Q: Find the values of a and b that make f continuous everywhere. a = II f(x) = x² - 4 X-2 ax² 4x = a +…

A: Given function:- fx=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;34x-a+bif x≥3

Q: 1. For each function below, determine whether it is discrete or not. Then, explain your choice. (61)…

A: 1(a) the first graph shows only the points , it does not include the values in between the points.…

Q: Find the interval on which f(x)%= -X xe is increasing. a. (-00,1] b. (-0,2] c.(-0,3] d. [1.2]

A:

Q: a. Consider the interval between x = -8 and x = -3. Explain why the product of the linear factors…

A:

Q: Which among the interval whose f(x) is increasing? а. (0,5) b. (-4,0) с. (5,7) d. (-7,-4) e. None of…

A: The function y=fx is an increasing function if x increases then y also increases. that means if we…

Q: Zx? +5x-75 Let fl)- X-5 a that f hgs a femovable disqontinutyy at 5 d delermine the value for HS)…

A:

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: True or False?: If f"=0 for some c, then f will have a point of inflection at c. Explain

A: Given the statement " If f"=0 for some c, then f will have a point of inflection at c ". We need to…

Q: Determine where f is increasing f(x) = I x+ 1 I

A: fx=x+1 It can be written as, fx=-x+1   when  x+1&lt;0x+1        when  x+1≥0     ∵x=-x   when…

Q: Decide if f(x) is uniformly continuous on the interval. Explain

A:

Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

Q: Q5. Explain why f(x) is not continuous at a. x2 - 25 f(x) = x + 5 if x #-5 a = - 5 if x =-5

A:

Q: II. Consider the function x<-2 -2 sxS1 1<x x+2 Determine if f(x) is continuous over the given…

A: