Let A(x)=∫(bounds 0 to x) f(t)dt, with f(x) as in figure.
Let A(x)=∫(bounds 0 to x) f(t)dt, with f(x) as in figure. Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5 Let A(z)...
You have 3 attempts remaining. Let A(x) = S6 f(t) dt, with f(x) as in figure. A7- LL 1 1 1 A(x) has a local minimum on (0,6) at 2 = A(z) has a local maximum on (0,6) at x =
Let F(x) = f f (t) dt for 2 in the interval (0,3), where f (t)is the function with the graph given in the following diagram. Ne 1 37 - 1 -2 Which of the following statements are true? Select all that apply. Fhas a local maximum at 2. F has a local minimum at 2. F is increasing on the intervals (0,0.5) and (2.5, 3). Fis decreasing on the interval (1.5, 2.5).
rt) dt, where f is the function whose graph is shown. /, 0 Let g(x)- f(t) 2 (a) At what values of x do the local maximum and minimum values of g occur? Xmin xmin = xmax = Xmax (smaller x-value) (larger x-value) (smaller x-value) (larger x-value) (b) Where does g attain its absolute maximum value? (c) On what interval is g concave downward? (Enter your answer using interval notation.) (d) Sketch the graph of g. 0.5 -0.5 2 46...
(1 point) Let F(x) = [” f(e) dt, where f(t) is the graph in the figure. Find each of the following: A. F(3) = B. F'(5) = C. The interval (with endpoints given to the nearest 0.25) where F is concave up: 1 2 4 6 7 interval = (Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10), or enter none for no intervals.) D. The value of x where F takes its maximum...
5pt 1. Let g() = | f(t) dt, where f is the function whose graph is shown below on the interval [0, 5). The graph consists of two straight line segments. - - - ------ -1- - - - - - --1- - -1- - - - - - - (a) Find g(1) and g(3). (b) On what interval(s) is g(x) decreasing? (c) At what x-value(s) in (0,5) does the local maximum of g occur? (d) At what x-value(s) in...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
(1 point) Let F(x) = ļ," f(t) dt, where f(t) is the graph in the figure. Find each of the following: 2 A. F(2) = 0 B. F'(4) = 2 5 69 7 C. The interval (with endpoints given to the nearest 0.25) where F is concave up: interval = (1.5, 4.5) (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8] or (1,5),(7,10), or enter none for no intervals.) D. The value of x where...
Consider the figure below. y=f(x) Evaluate. 1 ['rs. O 2. /Ral dx = 0 Let A(x) = f(t) dt for f(x) as shown in blue in the figure below. y = f(x) + X 2 3 4 5 6 7 1 Calculate the following. A(2) = A(4) = A(2) = A (4) =
7) Let O S Rn be open and suppose f : O → R is differentiable on O. Suppose has a local maximum or minimum at zo E O. Prove that f'(zo) = 0. 7) Let O S Rn be open and suppose f : O → R is differentiable on O. Suppose has a local maximum or minimum at zo E O. Prove that f'(zo) = 0.
The graph of f is shown to the right. The function F(z) is defined by F(z) = f f(t) dt for 0 x 4. a) Find F(0) and F(3). 2 b) Find F (1). c) For what value of z does F(z) have its maximum value? What is this maximum value? d) Sketch a possible graph of F. Do not attempt to find a formula for F. (You could, but it is more work than neces- sary.) -1 The graph...