2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are two distinct real numbers x1 and x2 such that f'(x1) = – f'(x2).

Q: Use geometric mean to find the value of x

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: To satisfy the criteria of mean value theorem the function must be continuous in the closed interval…

Q: Use the Mean Value Theorem to show that 1+x 0.

A:

Q: Apply Chebyshev’s rule with k = 5 and interpret your answer.

A:

Q: 8 Use right endpoints and 3 intervals to estimate S dx. 2

A:

Q: Use meau value theorem ex > 1+x for

A: The Mean Value Theorem states that if a function f   is  continuous   on   the closed interval [a,b]…

Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

A:

Q: Aresearcher studies water clarity at the same location in a lake on he depth (in inches) at which it…

A: This is a pair test. sample size (n) = 6 mean (d̄)       =  Σd/n                          = -23.9/6…

Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: At how many points on the interval [−2π, 2π] is the line tangent to f(x) = x + sinx parallel to the…

A:

Q: Use the Midpoint Rule with N = 10, 20, 30, and 50 to approximate the given curve's length. %3D c(t)…

A: We are given the curve :c(t)=(cos t, esint) The length of the curve: s=∫02π-sin t2+(cos t esin t)2…

Q: Show p V (p ^ r) is equivalent to p.

A: We have to show p∨p∧r. We will show this using truth table. p r p∧r p∨p∧r T T T T T F F T F…

Q: Year, x 56 57 57 61 61 64 67 68 70 Time, y 55.4 55.2 54.6 54.4 53.6 52.9 52.6 52.2 51.9 75 75 76…

A: Scatter plot shows the relationship between two variables. It uses dots to represent two different…

Q: Let f(x) = – 3 sin( – 2x – 5) – 6?

A:

Q: Why do you need continuity to apply the Mean Value The Why do you need differentiability to apply…

A:

Q: State and prove the intermediate value theorem.

A:

Q: Find the value of c guranteed by the Intermediate Value Theorem ( explain why is is guranteed).

A: Given:

Q: Whih conchason best describes her results? O 25% of the pens are black O 17% of the pens are red. O…

A:

Q: normally distributed with mean and standard deviation 15. domly selected person has an IO between…

A: Given data,Mean μ=100sd σ=15P(100<X<115)=?

Q: (a) g(a) and f(b) = g(b` %3D

A: Define h(x) as h(x)=f(x)-g(x). As both f(x) and g(x) are differentiable, we get h(x) is also…

Q: The Mean Value Theorem is used in many other theorems. Name three other theorems that require the…

A:

Q: es. show how the values are acquired.

A: Spray 1 0.693 0.405 0.405 0.405 -0.51 -0.92 Spray 2 0.588 0 0 -0.51 -0.69 -1.2 Lotion 1.386…

Q: Find the Fourier series of period 2n for the function scos x – sin x, (cosx + sin x, - n<x<0 0 <x<n°…

A: As per instruction we are allowed to answer only one question. The fourier series of a function  is…