Question: Suppose f is a polynomial function. If f (2) = 7 and f (6) = 1, then the Intermediate Value Theorem guarantees which of the

Suppose f is a polynomial function. If f (−2) = 7 and f (6) = −1, then the Intermediate Value Theorem guarantees which of the following? Justify your answer.

(a) f (0) = 0

(b) f (c) = 3 for at least one number c between − 2 and 6.

(d) − 1 ≤ f (x) ≤ 7 for all numbers in the closed interval [−2, 6].

Step by Step Solution

★★★★★

3.39 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The Intermediate Value Theorem states that if a function is continuous on a closed interval a b and ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

In Exercises 1-2, (a) use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a...

A sample containing an alkali sulfate is dried, weighed and dissolved in dilute HCl. Barium chloride solution is added in excess to precipitate barium sulfate, and the precipitate is digested in the...

Suppose that a function f is continuous on [0, 1] except at 0.25 and that f (0) = 1 and f(1) = 3. Let N = 2. Sketch two possible graphs of f, one showing that f might not satisfy the conclusion of...

questions are split now please help solve them please Question 43 Given P(I) = c' + x2 + 25x + 25, find the zeros, real and non-real of P The zeros are Write P in factored form (as a product of...

Evaluate p(x) = x3 - 9x at -4 and -2 to determine if the Intermediate Value Theorem guarantees that a zero exists between the two values. c) Does the Intermediate Value Theorem guarantee that a zero...

..Question 5 sample 1. Find the linearization, L(x), of the function f(x) = cos(2x) at a = =. 2. Find all critical points of the function f(x) = Vx - 3x - 10. 3. Find all intervals where the function...

5. PLease 15. Find all intervals where the function f(x) = 3x3/3 - 3x-1/3 is increasing. 16. The function f is defined by f(x) = (2 + 1)3 (x - 1)2 Its derivative is f'(x) = (2+1)'(x -5) (x - 1)3 Find...

hi ive attached a few more questions, thanks again 3 Question 1 0.5 pts Algebra Review. Consider the plot of the linear function below. Which of the following represents ths slope of this line? Om=3...

[re] 2 f3\" met" 6:3 am, what is Fr (x)? C) 11433? 61,3 e) O 0 11191195 13:2) 3)? 6(m 3)3 3) O 1n{3(37) 5(33) 3) 4. For the function F [551\") = If; Ina) (it, evaluate F 1(2). 0 23 111(2) 0 32 111(2)...

18. Let f be the function defined by f (xx) = Vl=+3 Which of the following statements is true? O f is not differentiable at a = -3 O lim+ + 3 f (x) 40 O f is not continuous at c = -3 O = = -3 is a...

Portelli Services provides room-cleaning arrangements for hotels in Pennsylvania. On April 1, Silvia Hotels & Resorts signed an agreement to outsource its room-cleaning functions to Portell. The...

A random sample of nurses working night shifts were asked whether they were fatigued (no or yes) and what form of sleep aid they used. Assume that each person used one sleep aid. The table shows the...