The graph of f’, the derivative of the function f, is shown above. If f(0) = 0, which of the following must be true? I. f(0) > f(1) II. f(2) > f(1) III. f(1) > f(3) A) I only B) II only C) III only D) I and II only E) II and III only

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Please provide me with the solution to this problem. Please show the work and try to dumb it down so…

A:

Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

A:

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: Find the derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

A:

Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

A:

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: First we have to find the function f(x).

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

A:

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

A:

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

A:

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

A:

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

A:

Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

Q: What is the derivative of f(x)=2sin(x) at the point x=−π/2?

A: To find the derivative of fx=2 sinx, at the point x=-π2.

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: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

A:

Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A:

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

A:

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Find the Derivative of the given function. If f(x) = -3, then f'(z) = %3D

A: Given f(x)=-3

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

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

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2

Q: If function f(x) is not continuous at the value x = a then the derivative of f does not exist at x =…

A:

Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2

Q: A function at x=2.1 , 2.2 , 2.3 has values 22, 18 , 16 respectively . the most accurate first…

A: the values f(2.1)=22,f(2.2)=18 and f(2.3)=16 the derivative…