Consider the function f defined by f(x) = 1/3x3 + 1/2x2 − 6x + 8. Find the following:  a. the intervals on which f is increasing b. the intervals on which f is decreasing

Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

A:

Q: Find the interval on which f is increasing and in which interval f is decreasing

A:

Q: DETERMINE WHETHER THE GIVEN FUNCTION m(x) IS CONTINUOUS OR DISCONTINUOUS AT x = -1

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

Q: Given the function f(x) = 2x + 6x?, determine all intervals on which f is both decreasing and…

A:

Q: find the intervals on which the function f(X) = x3+5x2-8x+1 is strictly increasing function

A:

Q: Find the intervals on which f(x) = x4 is increasing  and the intervals on which it is decreasing.

A: Given function:

Q: a)= 3ス2-3 %3D

A:

Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: 10 The function f(x) = - has a removable discontinuity at x = 2. To remove the - 2 discontinuity,…

A: Given: f(x)=10x+x2−4x−2

Q: Consider the function f(x)=5x+6x^2 over the interval [0,1].

A: Given that :-         f(x) = 5x+6x2 over [0,1] (a)  By deviding the interval into n sub intervals of…

Q: Use the first and second derivatives of f(x) = x³ – 3x² + 1 to determine the intervals on which f is…

A:

Q: Let f be defined as follows: x2 +5 for x > 5, Зах f(x)3D for xs5 For what value of a is the function…

A:

Q: Let f (x) = x³ + x° + 2x – 1. The function f is increasing on the following interval(s):

A:

Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

A:

Q: Determine the interval(s) on which the following functions are continuous. x + óx + 17 flx2 = x² - 9

A: Given The function is

Q: Find all the intervals at which the given function is continuous. 1. f(x)=x^2 - 3x - 10

A: Continuity: A function is said to be continuous at if following conditions holds. 1) exists 2)…

Q: find the intervals on which the function f(X) = x3 +5x2 -8x+1 is strictly increasing function

A:

Q: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Determine whether the following function is continuous at a. f(x) = /x- 7; a = 1

A: Topic :- Continuity

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing.…

A: solution is given by

Q: b. Determine the discontinuities of the following functions and state why the function fails to be…

A: i) F(x)=x3-x2-1ii) F(x)=x2-10x+2

Q: Show that the following continuous function has a root between l and 2. f(x) = 4x - 6x² + 3x - 2

A:

Q: Consider the function f(x) = 1 - 7x² OI function on this interval, i.e. f(3)-f(-4) 2 4)

A: answer is in next step . please give a like !!

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

A:

Q: Find the interval on Which f` is increasing and the interval of which f`is decreasing

A:

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

A:

Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x<-1, x>12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: Find the absolute extrema of f on the given closed interval. 1. f(x)= x³ + 3x² - 9x ; [-4,4]

A:

Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

A:

Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

A:

Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: For all x in the domain of the function –* , x+1 this func- tion is equivalent to:

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Are there any values of r for which the function A is discontinuous? Why?

A: We have to find out

Q: Find the domain of the function using interval notation. f(x) = -2x (1- 1) (r – 7) To enter oo, type…

A:

Q: The piecewise function f(x) is defined below. f(x) = {kx² - 4, Is-2 x+ 2, xS-2 x>-2 For what value…

A:

Q: Find the intervals on which the function f(x) =x3+5x2-8x+1 is strictly increasing function

A: ⇒f(x)=x3+5x2-8x+1⇒f'(x)=ddx(x3)+5ddx(x2)-8ddx(x)+ddx(1)⇒f'(x)=3x2+10x-8⇒f'(x)=3x2+12x-2x-8⇒f'(x)=3x(…

Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

A:

Q: Determine the discontinuities of the following functions and state why the function fails to be…

A:

Q: Determine if the function is continuous at the given point. 1 f(x) = {* - (x2 – 2 x 0 at x = 0.

A:

Q: On what intervals is the function f(x) = x-4r both decreasing and concave up? Write your answer in…

A: fx=x4-4x3 Differentiating with respect to x, we get f/x=4x3-43x2    ∵dxndx=n·xn-1=4x3-12x2 Again…

Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

A:

Q: f(x) = x² – 3x – 10 %3D

A: The limit of a function at a point is the value of the function when the value of the variable is…

Q: Determine the interval(s) on which the function is (strictly) decreasing.

A: We need to find the intervals on which the given function is strictlydecreasing.