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May 22, 2024 · Solved Examples on Concavity. Example 1: Determine the intervals where the function f(x)=x 3 −6x 2 +9x+15 is concave up and concave down. First Derivative: f'(x)=3x 2-12x + 9. Second Derivative: f"(x)=6x-12. Find Critical Points for Concavity: Set the second derivative equal to zero to find potential points of inflection: 6x-12=0. x=12/6=2
- Concave Function
Practice Questions on Concave Function. 1. Prove that f(x) =...
- Convex and Concave Functions
Convex and Concave Functions. Last Updated : 22 Sep, 2024....
- Concave Function
- Exercise 2: Create A Function with Variable Length of Arguments
- Exercise 3: Return Multiple Values from A Function
- Exercise 4: Create A Function with A Default Argument
- Exercise 6: Create A Recursive Function
- Exercise 7: Assign A Different Name to Function and Call It Through The New Name
Write a program to create function func1()to accept a variable length of arguments and print their value. Note: Create a function in such a way that we can pass any number of arguments to this function, and the function should process them and display each argument’s value. Read: variable length of arguments in functions Function call: Expected Out...
Write a program to create function calculation() such that it can accept two variables and calculate addition and subtraction. Also, it must return both addition and subtraction in a single return call. Given: Expected Output Expected Output:
Write a program to create a function show_employee()using the following conditions. 1. It should accept the employee’s name and salary and display both. 2. If the salary is missing in the function call then assign default value 9000 to salary See: Default arguments in function Given: Expected output:
Write a program to create a recursive function to calculate the sum of numbersfrom 0 to 10. A recursive function is a function that calls itself again and again. Expected Output: 55
Below is the function display_student(name, age). Assign a new name show_tudent(name, age)to it and call it using the new name. Given: You should be able to call the same function using
Jul 30, 2024 · Practice Questions on Concave Function. 1. Prove that f(x) = -x² is a concave function. 2. Is the function f(x) = ln(x) concave? Justify your answer. 3. Show that the sum of two concave functions is also concave. 4. Determine if f(x) = √x is concave on its domain. 5. Prove or disprove: If f(x) is concave, then -f(x) is convex. 6.
Sep 22, 2024 · Convex and Concave Functions. Last Updated : 22 Sep, 2024. In mathematics, convex and concave functions are functions with different curvature of graphs. A convex function curves upwards, meaning that any line segment connecting two points on the curve will lie above or on the graph.
- Reverse each word of a string. Given: str = 'My Name is Jessa' Expected Output. yM emaN si asseJ. Show Hint. Use the split() method to split a string into a list of words.
- Read text file into a variable and replace all newlines with space. Given: Assume you have a following text file (sample.txt). Line1 line2 line3 line4 line5.
- Remove items from a list while iterating. Description: In this question, You need to remove items from a list while iterating but without creating a different copy of a list.
- Reverse Dictionary mapping. Given: ascii_dict = {'A': 65, 'B': 66, 'C': 67, 'D': 68} Expected Output: {65: 'A', 66: 'B', 67: 'C', 68: 'D'} Show Solution.
Example. Let's see an example of concave function: Commonly, we can say that the convex functions are curved functions that are first decreasing and afterwards increasing, while the concave functions are the other way round, they are first increasing and afterwards increasing.
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The mathematical definition of a function being concave between points $x_1$ and $x_2$ is the following: $\lambda f(x_1)+(1-\lambda)f(x_2) \leq f(\lambda x_1+(1-\lambda)x_2)$, for any $0 \leq \lambda \leq 1$. Can someone give a detailed, intuitive explanation of this theorem?
