if true: explain why the statement is true for all cases • if false: disprove with a counterexample. Show how your example disproves the statement Note: examples can not prove statements true, but they may be useful in accompaniment with your explanation 'If a function is increasing over its entire domain, it will not have a critical number."

Q: Plot the function using a graphing utility and find its critical points and extreme values on [−5,…

A:

Q: Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat's…

A: Critical number: A point c is said to be a critical number of a differentiable function f, if f'c=0.…

Q: On which the interval the function is increasing?

A: Given,          The graph of the function is shown below :

Q: Determine the intervals where the function f(x)= lnx/x is increasing and where it is decreasing.

A:

Q: Show that differentiation reverses parity: If f is even, then f' is odd, and if f is odd, then f' is…

A: To show that if f is even then f' is odd  and if f is odd then f' is even

Q: On which two intervals is the function increasing (enter intervals in ascending order)? to

A:

Q: True False Suppose f(x) is continuous everywhere. Must f(x) attain an absolute maximum somewhere on…

A: Extreme value theorem states that if f(x) is continuous on closed interval I, then f(x) attains…

Q: What does it mean for a function to be continuous on an interval? Give examples to illustrate the…

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A:

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: Given:   To find:      The critical numbers of f ( x ). (a) The open interval on which the function…

Q: Sketch the graph of a function f that is continuous on [1,5] and has the given properties.…

A: At minima and maxima, the slope is zero.  Absolute maximum: The maximum value of the function in the…

Q: How do you find the length of the graph of a smooth function over a closed interval? Give an…

A: known fact:

Q: continuous at x- 3? Why or why not? Is the function given by f(x) = ! 3*+5, for x 3,

A:

Q: What does it mean for a function to be continuous on an interval? Give examples to illustrate the…

A: In simple terms, if the graph of a function can be drawn without lifting the pen from the paper, we…

Q: Considering the following,  -Describe the interval(s) on which the function is continuous.…

A: Continuous Function: The function f(x) is said to be continuous if for every c in the domain of f,…

Q: How do i figure out whether this function is continuous or not (proving it) without given at which…

A:

Q: Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat's…

A: This Fermat's theorem gives the emphasis at graphing of any function Consider a graph which is…

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: fx=−3x2−4x−2 To find: (a) open interval on which function is increasing and decreasing (b) Apply…

Q: The vertical line test to determine whethera curve is the graph of a function states: If every…

A: We have to prove that a vertical line in the xy plane intersects a given curve in at most one point…

Q: find the critical numbers of f (if any), (b) find the open interval(s) on which the function is…

A: Given information: fx=-2x2+4x+3 (A) To find the critical number derivate the function and then…

Q: determine the points of discountinuty of the function f(x)=-x squared and nature of discountunuity…

A: f(x) =  -x2  We can plot this curve as

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: fx=-2x2+4x+3 Now critical numbers are the numbers for which first derivative is zero. So…

Q: Suppose a function is always decreasing (example graphed below) and we estimate the net signed area…

A: Observe the following. Fro m the above graph, it can be observed that the actual area overestimate.

Q: Find all the critical points of the function ?(?) = ?^25 − ?^9 . Use the First and/or Second…

A:

Q: Find the critical points of the function. Then use the Second Derivative Test to determine whether…

A:

Q: y = on [1, 3]

A: Graph of the function is shown

Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

A:

Q: Find the open interval(s) where the function is increasing and decreasing. f(x) = - x + 3 Show work…

A: For a function f(x): f(x) is increasing in the interval where f'(x) >0 f(x) is decreasing in the…

Q: 5. What is odd and even function?

A: We have to define odd and even function.

Q: Aside from Extreme Value Theorem, there is another theorem behind optimization, the Fermat’s…

A: Since interval is open and c in the interval this excludes c being one of the interval limits.   If…

Q: Use the second derivative test to find the location of all local extrema in the interval (2) for the…

A: We can solve as follows

Q: What doe the “sufficiently well behaved” function implies?

A: Generally the functions defined or behave well when the given function is well defined in the domain…

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: Given that f(x) = (x2 − 2x + 1)/(x + 1) We need to: 1) find the intervals in which function is…

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A:

Q: The graph below is the graph of the First Derivative of f(x)... that is it is the graph of f '(*).…

A:

Q: What does it mean for a function to be continuous on an interval?Give examples to illustrate the…

A: For open intervalIf f:(a, b)→ℝ is defined on an open interval, then f is continuous on (a, b) if and…

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A: given function     y = x5/2 -2x2 ,  x > 0

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A:

Q: Sketch the graph for this function

A: In this question. we draw the graph by using the calculus method i.e. by finding intercepts,…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: True or False The cube function is odd and is increasing on the interval (-∞,∞)

A: Explanation:' The cube function is f(x)=x3 An odd function is the function that satisfy this…

Q: For the function attached, please find all critical points (determine if they are local…

A:

Q: (4) Is it possible to define a function which is continuous on a closed, finite interval but does…

A:

Q: Sketch the graph of a function f that is continuous on [1,5] and has the given properties.…

A: Consider the equation

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: Function: f(x)=|x+3|-1 c) The graph of the function is:

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: Consider the given function: fx=x2x2+4 Differentiate the function with respect to x:…

Q: true or false? if a function is differntiable at an input then it must be continuous at the input

A: Consider the given proof. Statement: If f is differentiable at a then f is continuous at a.

Q: 3. True or False: Mean Value Theorem is applicable to f in the interval [0,2].

A: This question is related to mean value theorem. We will solve it using given information.