7. For the function f (x) = In(x² + 1) (a) find all intervals where f is increasing, (b) find all intervals where f is decreasing,

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

A:

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

A:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

A:

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: If f(x) = 2+ |x − 3| for all x, then the value of the derivative f’(x) at x = 3 is

A: Given;. f(x)=2+|x-3| f'(x)= ?

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

A:

Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 f(æ) = 6x – k x <4

A:

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

A:

Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above…

A:

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: 6. Find the absolute extrema of the function on the closed interval given: f(x) = 2x/2 – x; [ –2,1]

A: Pue derivative zero, if value lie in interval then put in function for maxima and minima

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: -7 if x 2. Sketch the graph of the function and use the limit definition of the derivative to show…

A:

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

Q: For the function f(x)=6x+2sin(x)f(x)=6x+2sin⁡(x), find all intervals where the function is…

A:

Q: 19 – x² ; if x 3 continuous or not on the interval [0, 3].

A: Given function: fx=9-x2;if x≤3x-3;if x&gt;3 The objective is to determine if the function is…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

A:

Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: 6. Find the length of the curve given by the graph of the function f(x) = x/x, for x in [1,4].…

A:

Q: 1. Identify all the x-values of the candidates for where you might find an absolute maximum or…

A:

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

A:

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

A: Given,  fx = x2-4x+9    We have to find the absolute extremum values in the interval 1, 4

Q: 2. (a) Give the definition of the derivative f'(x) of the function f(x) in terms of a limit. (b) Use…

A:

Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

A:

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

A: limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

A:

Q: x+4 if x2

A:

Q: (2x - 2 x² - x f(x) = x² 4 graphing calcu x 2 x = 2

A:

Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given, f'x=21-x21+x2                         ...(1) and f''x=4xx2-31+x22

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…