b) Let f(x) = x*(x? - 1) be a given function then i) FIND the intervals on which function is increasing and decreasing. i) IDENTIFY function's local and global extremum.

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Use the First Derivative Test to find relative (local) maximum points points, if any, of the given…

A: given

Q: Let f(x)= x2 -3x + In x. Find the local maximum and minimum values of f by using the second…

A: Since, we are given f(x)=x2-3x+ln x and our aim is to find the local maximum and minimum values of f…

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

A:

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

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

A:

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

A: Given Data The equation is f(x)=x²+6x+10.   (b) Differentiate the equation with respect to x and…

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

A:

Q: Let f (x) = x³ – a* with domain (-∞, ∞0). Find the intervals where f is increasing and where f is…

A: Given,           fx=x3-14x4 with domain -∞,∞.

Q: Verify Mean value theorem for the function f(x) = 4x³ + x + 3 over the interval [0, 1].

A: Given: f(x)=4x3+x+3, 0, 1

Q: 2. Let f(x) = Determine the exact location of any turning points. Use the second derivative to…

A: We can solve this as follows:

Q: 2. Use the second derivative to determine the intervals where f(x) = -2x³ + 4x2-150x is concave up…

A:

Q: Verify Mean Value Theorem for the function f (x) = -6x+x³ over the interval [1,3]. %3D

A:

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: Determine where the absolute extrema of f(x) =--5x + 14x on the interval 1, 3] occur. 1. The…

A: Given function is

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: Determine the open intervals on which the graph of the function is concave upward or concave…

A: y=x+2sin x Let take first derivative y=x+2cscxy'=1-2cotxcscxNow take second…

Q: Find the absolute extreme values of the function on the interval f(x)=tanx, -pie/6 less than or…

A: To find the extreme values of the function on the interval, f(x)=tanx, -π6≤x≤π6

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

A:

Q: Find the points at which the function f (x) is continuous and the points at which f is…

A:

Q: Determine the point(s) at which the given function f(x) is continuous. f(x) = /5x+ 15 Describe the…

A: Rule: A function f(x)=x is said to be continuous when x≥0.

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

A: We find the critical points by solving f'(x)=0 Answer(a):  Critical numbers= -1.633 and 1.633

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

A: Given: fx=8-xx+12

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

A:

Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

A:

Q: check uniquness and existance for fixed point while f(x)=(2x+1)^-3 in [1,2]

A:

Q: What conditions must be satisfied by a function if it is to be con-tinuous at an interior point of…

A: A function is continuous at an interior point c of its domain if

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A:

Q: Find the absolute minimum and absolute maximum values of f on the given Interval. f(x) = In(x2 + 3x…

A:

Q: 2. Let f(x) =- 3-2x Use the definition of the derivative to find f'(x). Show complete work,…

A: The given function is f(x)=x23-2x.

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 thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x<4we find constant 'a' such that the function is continuous…

Q: Find the absolute minimum and absolute maximum values of f on the given interval f(x) = x - In(2x),…

A: see next step

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

A: Given function is f(x)=x2-6x+5 The first derivative of the function is given by f'(x)=2x-6 So the…

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

A:

Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

A:

Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

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

A: To find the critical points we solve f'(x)=0

Q: Use second derivative test, If f(x) = 36x + 4 then f(x) has a local 3 maximum at the point O x = -7…

A: Here we need to find the local maxima of the function.  The solution is following .

Q: Determine the intervals of concavity for the function f(x) = xex .

A:

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

Q: What does it mean for a function to have an absolute extremevalue at a point c of an interval [a,…

A: When an output value of a function is a maximum or a minimum over the entire domain of the function,…

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

A:

Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

A:

Q: 9. Given the function f(x) 3x*-4x2 +2, use the first and second derivative tests to find: a) the…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.