The graph of f', the derivative of the function f, is shown below. Determine all intervals on which f(a) is concave up on the open interval (-9, 9). Graph of f" 10 9 to -1 10 -1 -3 -5 -6

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: 5. Use the limit definition of derivative to find f'(x) if f(x) = VT.

A:

Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

Q: Define the derivative f'(a) in your own words. Mention two ways of interpreting this number.

A: We need to describe the term f'a, and the way to evaluate f'a.

Q: Use the limit definition of derivative to find the derivative of the function with respect to x.…

A:

Q: Let f be a differentiable even function. By use of the definition of the derivative directly, prove…

A: AS we know what are even and odd function. Even Function  f(-x)=f(x) Odd Function f(-x)=-f(x)

Q: I dont know how to find the derivative of the function using the definition of derivative. And…

A: Given that: f(x)=1x2-4

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A:

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We need to find the derivative of the function F(x^4) with respect to x.

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A:

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: Differentiate the function with respect to x using the chain rule to find f'(x). According to the…

Q: Use the definition of a derivative to find f'(x) and f"(x). f(x) = 3x2 + 2x + 2 f'(x) = f"(x) =…

A:

Q: Use the graph of the function to sketch the graph of the derivative. (on the same grid is fine)

A:

Q: Use the limit definition of derivative to compute the derivative of ​f(x)equals=44xcubed3. Find…

A: From the given information:

Q: What rule must be applied in finding the derivative of f(x) = (3x^3-2x +1) (2x -3) * O…

A:

Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: Determine the open intervals on which the graph of the function is concave upward or concave…

A: y=x+2sin x Let take first derivative y=x+2cscxy'=1-2cotxcscxNow take second…

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

A:

Q: oFind the derivative: (show all 1. f(x) = 2xe-3x chou

A:

Q: Let f be a function. Explain, using any method , as to why f(x) and f(x) + 2 have the same…

A:

Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

A:

Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

Q: f(x) = tan (5æ).

A:

Q: Find the derivative of the function f(x) = {x3 - tan tan (4x2 -2)}4

A: The question is taken from the calculus in which we have to find the derivative of given function We…

Q: Calculate the derivative using the appropriate rule or combination of rules. f(x) = (x + 4)(x + 2)(x…

A: The derivative of the given function is solved below.

Q: Use derivative to identify open intervals on which the function is increasing or decreasing.…

A:

Q: Use the representation of the derivative as a limit to compute the derivative f′(x) of the function…

A:

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

A:

Q: Use one of the definitions of the derivative at a point to determine the slope of the tangent line…

A: The given function is fx=2x2-x at the point 1,1. Definition of the derivative at a point is…

Q: Differentiate f and find the domain of f. (Enter the domain in interval notation.) Rx) = 1 - In(x –…

A:

Q: Use the linut definition to Compute f(x) when f)-at. the derivative f(x) when f)-2+L

A:

Q: Use the limit definition of the derivative of a function to find the derivative of f(x) = 4x at x-5

A: From the given problem:   fx=4x2   From the limit definition of the derivatives:…

Q: use the derivative to identify open intervals on which a function is increasing or decreasing…

A: To find the interval on which the function is increasing or decreasing on using the derivative of…

Q: The derivative of f is equal to f'(x) = f(x)f(-x). Show that f' is not one-to-one. %3D

A: First we will find 1st derivative using the given relationship.

Q: Use the graph to estimate the open intervals on which the function if increasing or decreasing, Then…

A: Given that: The equation of the function f(x) =1(x+1)2 . Graph:

Q: Use the first derivative test and the second derivative test to determine where each function is…

A:

Q: Consider the function f (x) = x(Third digit of your ID number). Calculate the first derivative at…

A: Three point central difference formula.

Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

A:

Q: 4 3. Лх) — Зх - 5 %3D

A: Given that  f(x)=4/(3x-5)^2  To find the derivative of f(x)

Q: The rule of the derivative of a function f is given. Find the location of all points of inflection…

A:

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: Find the derivative of f(x) = (-x3 - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: The given function is: fx=-x3-2x2-2xsinx   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: Use the limit definition of the derivative to calculate the derivative of f f'(x) = f(x)=-3x³ - 2x +…

A:

Q: Show that F(x) = tan2 x and G(x) = sec2 x have the same derivative.What can you conclude about the…

A: Given:Fx=tanx2Gx=sec2x

Q: Use the fact that the derivative of the function f(x) =- is f'(x) = to find the equation of the…

A: We need to find the equation of tangent to the graph of f(x).

Q: Consider the function f (x) = x(Third digit of your ID number), Calculate the first derivative at…

A: Given that, Student id = 3 fx=x3The value of the first derivative at point x=3 is calculated…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.