4. True or False. Write true or false in the blanks.
a, A continuous function over a closed interval will achieve exactly one local maximum on that interval ______________
b. If f(x) and g(x) both have a local maximum at x=a then has either a local maximum or a local minimum at x=a. ___________
c. If for all x and if a > b, then _____________
d. If is undefined, and if is continuous at x=c, then has a local extrema at x=c. ________
e. If and is differentiable for all x , then for all x .__________
4. True or False. Write true or false in the blanks. a, A continuous function over a closed inter...
Put (v) for true and (x) for false sentences 1. () If f'(a) 0, then f (a) is a local extrema of f. 2. () A function on a closed interval must have a local extrema. 3. ( ) If f have a local max at x = a, then its square f2 must also have a local max at x = a as well 4. () If f and g have both local minima at a, then their sum...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Question 4* (Similar to 18.1) Suppose f is a continuous function on a closed interval [a, b]. In class, we proved that f attains its maximum on that interval, i.e. there exists Imar E la, so that f(Imar) > f(x) for all r E (a,b]. We didn't prove that f attains its minimum on the interval, but I claimed that the proof is similar. In fact, you can use the fact that f attains its maximum on any closed interval...
Consider the following graph of f(x) on the closed interval (0,5): 5 4 3 2 1 0 -1 0 1 2 3 5 6 (If the picture doesn't load, click here 95graph2) Use the graph of f(x) to answer the following: (a) On what interval(s) is f(x) increasing? (b) On what interval(s) is f(x) decreasing? (c) On what interval(s) is f(x) concave up? (d) On what interval(s) is f(x) concave down? (e) Where are the inflection points (both x and...
Write ‘T' for true or ‘F' for false. You do not need to show any work or justify your answers for this question. The questions are 2 points each. (a) __If (xn) is a convergent sequence (converging to a finite limit) and f:RR is a continuous function, then (f (xn)) is a convergent sequence. (b) _If (xn) is a Cauchy sequence with Yn € (0,1) and f :(0,1) + R is contin- uous, then (f(xn)) is also a Cauchy sequence....
true or false The real valued function f : (1,7) + R defined by f(x) = 2is uniformly contin- uous on (0,7). Let an = 1 -1/n for all n € N. Then for all e > 0) and any N E N we have that Jan - am) < e for all n, m > N. Let f :(a,b) → R be a differentiable function, if f'() = 0 for some point Xo € (a, b) then X, is...
Let Which of the following are TRUE? Select ALL that apply. Please show all your work. a. has a local maximum at whenever is an even integer b. has a saddle point at whenever is an even integer c. has a saddle point at whenever is an odd integer d. has a local minimum at whenever is an odd integer fr, y) = sin(x + 7/2) +y? We were unable to transcribe this imageWe were unable to transcribe this imageWe...
Determine whether the statement is TRUE or FALSE. You are NOT required to justify your answers. (a) Suppose both f and g are continuous on (a, b) with f > 9. If Sf()dx = Sº g(x)dx, then f(x) = g(x) for all 3 € [a, b]. (b) If f is an infinitely differentiable function on R with f(n)(0) = 0 for all n = 0,1,2,..., then f(x) = 0 for all I ER. (c) f is improperly integrable on (a,...
Are the following statements true or false? Justify your answer. (i) If f(x) > 0 for all x ∈ [a, b] with a < b, then f(x) dx > 0. (ii) If f(x) dx < 0 then f(x) < 0 for all x ∈ [a, b]. We were unable to transcribe this imageWe were unable to transcribe this image
Problem 1: Determine whether the statement is true or false. If the statement is true, then prove it. Otherwise, provide a counterexample. (a) If a continuous function f:R +R is bounded, then f'(2) exists for all x. (b) Suppose f.g are two functions on an interval (a, b). If both f + g and f - g are differentiable on (a, b), then both f and g are differentiable on (a,b). Problem 2: Define functions f,g: RR by: x sin(-),...