Consider all of the possible relations between z and y such that y varies at a constant rate of change of 5 with respect to z. Which of the following must be true in ALL of those possible constant rate of change relations between these two variables? Hint: Think about the graphs of several relations that all have a constant rate of change of 5. Which of the following conditions must be true for ALL such graphs that you can draw? OAy - Az OAy - 5Az Oy-5z OAz - 5Ay Oy-5Az

Q: Which of the following is the absolute minimum value of the fuk took f(x)=(x-3)^3 on interval [1,4]

A: The graph is shown below:

Q: Consider the graph of a function. 4 3+ 1 + + 4 6. 5 1 2 3 Find the point c at which the function has…

A:

Q: If f'(x) and g'(x) exist and f'(x)> g'(x) for all real x, then the graph of y f(x) and the graph of…

A: Given f'x>g'x

Q: use the graphs to find a δ > 0 such that| ƒ(x) - L | < ∈ whenever 0 < | x - c | 6 δ

A:

Q: Suppose that h(x) = f(x) / g(x) . The function f can be even, odd, or neither. The same is true for…

A:

Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: Which of the following represents a family of quartic functions with zeros -1(order 2), 2, and 3

A:

Q: If g(x) is an odd function defined for all values of x , can anything be said about g(0) ,Give…

A:

Q: f(x) = (x +2)²(x – 1) f'(x) = 3x(x+2) f"(x) = 6x +6 %3D

A:

Q: Look at the given graph of the function V(x) from question 1 above. 150- -140+ -10- -120 -110 -100-…

A: By observing the graph ;

Q: Given this graph of y = f(t): -1 -2 -3 if A(x) | f(t) dt then: А(1) А (1) -

A: In this question we have to find A(1) and A'(1)

Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: Chapter 4, Section 4.1, Question 040 Sketch a possible graph of y =f (x), using the given…

A: Take function  f(x) = x3   Then we know that  f'(x) = 3x2 and  f''(x) = 6x

Q: 1) Find a function y whose graph passes through the point (1, ) and satisfies x?y' = y.

A:

Q: 1) Find a function y whose graph passes through the point (1, and satisfies x?y' = y.

A: We have to solve

Q: х2+1 h(x): %3D х-5

A: A rational function is continuous for all real numbers except at which the denominator is zero.…

Q: If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x, then the graph of y f(x) and the graph of…

A:

Q: Under what circumstances is a linear function f(x) = mx + b odd? Can a linear function ever be even?

A: To check the linear function

Q: Which of the following statements is false for a function f that can be differentiated at least…

A: We have to define which statement is wrong

Q: Given the graph of y=f(x) below, at which of the marked x-values can the following statements be…

A:

Q: Find the minimum value for f(x) =– on - on (0, 2]. А. 2 В. 1 С. D. 2e e

A: Take the derivative of the given function, equate to zero and solve for x. Now put this x value in…

Q: By the Mean Value Theorem, we know there exists at least one c in the open interval (-4, 4) such…

A:

Q: Suppose g is a linear function such that g(1.1) = 3.3 and g(-4) = 7.2. Find the equation for g. (Use…

A:

Q: which of the following is true about the relation shown below?

A: The difference between a relation and function is, A relation can have many output for a single…

Q: Given the graph of y = f(x) below, at which of the marked r-values can the following statements be…

A: Since you have asked multi part question, we will solve the first 3 part of question for you as per…

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: Sketch a graph of S x2 f(x) = { if –1<x < 0 if 0 < x <1 2 – 3x and determine any absolute extrema on…

A: Consider the given function. fx=x2           if -1≤x≤02-3x    if      0&lt;x≤1 Now, draw the above…

Q: For what values of a and b does the graph of f(x) = a(x + b In(x)) have a local maximum at the point…

A:

Q: s(x) - [0,3] et 1+x²'

A:

Q: (4) Sketch the graph of a function f(x) satisfying (a) f(x) 2 and for x 0 for x between -1 and 2,…

A:

Q: Consider the graph below. 4) (1, 4) -1,52) (3.-4) (-4, 5) Determine if f is continuous at x = c. (a)…

A: Given  The graph of the function    Definition of Continuity :- A function f is continues at x= c…

Q: 12. The graph on the right is NOT differentiable at x = 1. For what reason is it not differentiable?

A: Yes, given graph is correct.Given function:f(x) = x-1f(x) = -x+1        x&lt;1x-1           x≥1

Q: 1. Let X be the graph of f(x) that is, X is the subset of R x R satisfying the given equation.

A: Sol

Q: The slope y-intercept form of a linear relation is represented by y=mx+by=mx+b.  Which equation…

A: Solution: The objective is to find equation shows x isolated correctly for this formula

Q: The graph of the second derivative, f"(x), is given. > 10 6 -1 -2 -4 -6 -8 -101 Determine the…

A:

Q: if r 4,

A: Given,          The function is gx=xif x≤03if 0&lt;x≤13-x2if 1&lt;x≤4x-3if x&gt;4

Q: 1) Consider the end behavior description below. • as x -, fx) - • as x, fe)-- Which function…

A: We need to select a function for which 1. As x→-∞, f(x)→∞ and 2. As x→∞, f(x)→-∞

Q: Suppose f(x) is a smooth function that passes through the points (3, –5) and (-6, 4). Prove that…

A: Given,        Suppose fx is a smooth function that passes through the points 3,-5 and -6,4.…

Q: If f (x) and g(x) then there exists a constant C such that f(x) = 9(x)+C, for all x. are two…

A: Let us consider h(x) = f(x) - g(x), Then h'(x) = f'(x) - g'(x) Since we have given f'(x) = g'(x),…

Q: Consider the graph of the function f(x) = 2 x^(5/3) - 5 x^(4/3), the relative minimum is located at…

A: Note :- A relative minimum of a function is all the points x, in the domain of the function, such…

Q: The following is a graph of a function g(x), defined on the interval [0,4] .

A: The graph of g(x) is as shown below :

Q: 11. The graph of a twice differentiable function, f(x), with a relative minimum at (–1, –2) is shown…

A:

Q: At which point is g(x) = 3x3 + 4x2 – 3x concave downward? (Refer to the graph of g(x) below.) 5-…

A:

Q: Question 4 Suppose f(x)=x+x3-6x2. Determine the value of x where fhas a relative maximum value. A…

A: x=-3 is the point of a relative maximum value

Q: 1) Find a function y whose graph passes through the point (1, 2) and satisfies x?y' = y.

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Given the graph of the derivative f'(x) shown below, which one of the following statements regarding…

A: Consider the provided graph,