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Graph off 2. The figure above shows the graph of f', given by f'(x) = ln(x2+1)...
Suppose that f(x) is a differentiable function such that the tangent line at x = 3 is given by y=-***. How many of the following statements MUST be true? I. According to the linearization of fat x = 3. f3.001) - 0.9989 IL (3) -0. III. f is concave down on an open interval containing x = 3. IV. The graph of y = f(x) attains a maximum value on the interval (-1,4). V. Applying Newton's Method to approximate the...
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...
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...
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...
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...
Can someone help me? I am not very familiar with the Newton method. The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x)- 0 with initial approximationx-6. 이 (a) Draw the tangent lines that are used to find x2 and x3, and estimate the numerical values of x2 and x3. (Round your answers to one decimal place.) x2 = x3 = The figure shows the graph...
Find the absolute maximum and absolute minimum values off on the given interval. F(x) - In(x2 + 5x + 12), (-3, 1] absolute minimum value absolute maximum value Need Help? Read T alk to a Tutor
Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y = Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y =
need hw help For the function f(x) = ln(x2+25). Find all interval(s) where f(x) is increasing. Select all that apply. (O, 5) (-0, 0) (-5, 0) ol-00,-5) None (0, 2) (5, 00) For the function f(x) = in(x2+25). Find all interval(s) where f(x) is decreasing.Select all that apply. (5, 0) (-00, 0) O (0, 5) (-0, -5) (0, 0) None (-5, 0) For the function f(x)=Ln(x2+25), identify any relative maximum or minimum point(s). Select all that apply. (21n(5), ) is...
9. Find the local/absolute extrema off on the closed interval; clearly label your solutions f(x)= x3 – 3x +1 (0,3]