Let f be continuous on an interval I from a to b with only one critical number c in (a, b). If f'(c) [Select] and f" (c) [Select] , then f(c) is the absolute minimum of f on I. If f'(c) [Select] ✓ and f" (c) [Select] , then f(c) is the absolute maximum of f on I.

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Suppose you know that the function f is decreasing and concave down on t interval [2, 7]. which of…

A: If the first derivative of a function is negative then the function is decreasing and vice versa.…

Q: Assume the functions below are continuous with domain all real numbers. (a) If f'(a) = 0, then x = a…

A: Given that:- The function is continuous with domain all real numbers

Q: Let X=[-1,1] and Y=[0,1], and define the function f:X-->Y by f(x)=x^2. Which of the following is NOT…

A:

Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

A: Solution

Q: let f(x) = 2x²-36x² + 20. Find the intervals where f is increasing. a) (-3,0)√(3, ~) b) (-3,0)0(0,3)…

A: Let To find the intervals where  is increasing.

Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: Let F ~ F4,5. Assume c₁ satisfies P(F > c₁) = 0.05 and P(F< c₂) = 0.05. Then, c₁ =_ and C₂ = (b).

A: It is given that F∼F4,5 c1 and c2 are two constants such that P(F&gt;c1)=0.05 and P(F&lt;c2)=0.05

Q: Use the graph of f' to identify the critical numbers of f, identify the open intervals on which f is…

A:

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: Consider the function f(x)=x/x^2+12x+32. Determine the intervals on which f is increasing and…

A: We have to determine the intervals at which the function  is increasing or decreasing.

Q: Let A = {1,2,3}. Define f: A  --> A by f(1) = 2, f(2) = 1, and f(3) = 3. Find  f^2 f^3 f^4. how…

A: Solution:-

Q: f'(x) +++0 0 +++, -8. -3 f"(x) 0 ++ 0. 0 ++++ -5 -3

A: