Let f(x)=x²+sin x+1 on the interval [1, 2]. Choose the correct statement below. O Since f is not continuous on [1,2], it does not attain its absolute maximum value nor its absolute minimum value. O By the Extreme Value Theorem, f attains both its absolute maximum value and its absolute minimum values. O Since f is not differentiable on [1, 2], it does not attain its absolute maximum value nor its absolute minimum value. O The function f attains only its absolute minimum value. O The function f attains only its absolute maximum value.

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: f(x) = 3x² - 2x-2, [-1,2]

A: To determine if the function   is continuous over the interval [−1,2], we need to check three…

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: 5. Let f be defined for all real numbers and suppose f(x)-f(y)| ≤ (x - y)² for all real numbers, x…

A:

Q: Show that the given function is analytic in an appropriate domain. 2- y S(x) = Tr+2}* +3y² (x+2)*…

A: Please consider the handwritten solution.

Q: 2. A continuous function f is defined on the interval [-2, 2]. The values of f at some of the points…

A: As per our guide line if multiple questions are posted we are supposed to answer only the first one…

Q: Find the absolute maximum and absolute minimum values of f on the given interval F(x) = xex2/98 [-3,…

A: Given function is

Q: 3) Let f'be the function given by (x-1)(x²-4). For what positive values of a is f continuous for all…

A: We have cheek the positive values of a is F continues for all real number

Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…