Graph off The function is defined on the interval -5 S figure above S where c...
4 -2 2. The function f is defined on the closed interval [-4,9]. The graph of f consists of a semicircle, a quarter circle, and three linear segments, as shown in the figure above. Let g be the function defined by g(x) = 3x + f(t) dt. (a) Find g(8) and g'(8). (b) Find the value of x in the closed interval (-4,9] at which g attains its maximum value. Justify your answer. (c) Find lim f'(x), or state that...
please explain in detail 4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be the function defined by g(x) = 5 +1.f(t) dt for-1 $154. (A) Find g(4). (B) On what intervals is gincreasing? Justify your answer. (C) On the closed interval 1 s xs 4, find the absolute minimum value of g and find the...
(-5,2) (-2,-1) Graph of g The continuous function g has domain -5 < x < 2. The graph of g, consisting of two line segments and a semicircle, is shown in the figure above. The graph of g has a horizontal tangent at x = -1. Let h be the function defined by h(x) = S-29(t)dt for -5 < < 2. (a) Find the x-coordinate of each critical point of h on the interval -5 < x < 2. (b)...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
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...
Graph off 2. The figure above shows the graph of f', given by f'(x) = ln(x2+1) sin(x*) on the closed interval (0,3). The function f is twice differentiable with f(0) = 3. (a) Use the graph of f' to determine whether the graph of f concaves up or concaves down on the interval 0<x<1. Justify your answer. (6) On the closed interval (0,3), find the value of x at which f attains its absolute maximum Justify your answer. (c) Find...
8. Consider the function f whose graph consists of four line segments and a semicircle as shown below. Define g(x) by g(x) = 5 f(t)dt. Note: The graph is of the function f. The graph of g is NOT shown to you. a) Find all values of x with –5 < x < 5 for which g'(x) = 0. Explain your reasoning. b) Find g(-1) and g"(-1). Show the work that leads to your answers. c) Find all values of...
Graph of f Let f be the continuous function defined on (-1,8) whose graph, consisting of two line segments, is shown above. Let g and h be the functions defined by g(x) = h (2) = 5e-9 sin 2. -x +3 and (a) The function k is defined by k (x) = f(x) g(). Find k' (0) (b) The function m is defined by m (x) = 2007). Find m' (5). c) Find the value of x for -1 <...
Consider the graph of the function g shown below. The domain of g is [0,10], and the graph of g is comprised of two line segments and a quarter circle. 1. The function F is defined on [0,10] . It is an antiderivative of g and satisfies F(7)=0. Sketch a graph of F 2. Use your knowledge of area to compute F(4). Explain your reasoning. 3. Write a formula for F using an appropriate integral of g. 4. The function...
Question 3 2 pts Please do not use a calculator for this problem. रिकार 2 2 3 4 5 (5.-1) Graph of f' Let f be a function defined on the closed interval -5 58s 5 with f(1) = 3. The graph of the derivative off, consists of two semicircles and two line segments, as shown above. (a) For -5 <x< 5, find all values x at which f has a relative maximum. Justify your answer. (b) For -5 <...