True or false: Suppose f(x) is a function that is differentiable everywhere. If f'(x) < 0 for all x, then f(2) must be less than f(3). Explain.

Q: what is derivative of f(x)=x/(x+1)^2

A:

Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

A:

Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

A:

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

A:

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

A:

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

A:

Q: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

A:

Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

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

A:

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

A:

Q: Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of…

A:

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

A:

Q: n(x)=3x?4k+1 %3D

A:

Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Gottfried​ Leibniz, one of the inventors of​ calculus, initially thought that the derivative of​…

A:

Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

A:

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

A:

Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

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: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

A:

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

A:

Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

A:

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

A:

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

A:

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.