The graph of of f(t) is given below. f(t) is a semicircle for 4 < t...
Find the following values Answer choices for C: Point of Inflection Local Max Local Min Zero Answer choices for D 1. is continuous is not continuous does not exist 5. POI local max local min zero The graph of of f(t) is given below. f(t) is a semicircle for 4 < t < 6. Let g(x) = { $(t)dt a. Find the following values. 1. g( - 1) = 2. g(1) = 3. g(4) = 4. 9(6) = b. 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...
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...
3. Let F(x, y) = (-y, x) and let C be the semicircle with parametrization f(t) = (4 cos t, 4 sin t) for 0 <ts. Compute ScF.T ds.
Could you label and explain how to get each term? Thank you! 3. Find the equation of the tangent line to the graph of f(x)-1+e 0 4 Graph the following function, using information such as intervals of increase and decrease, relative extrema, intervals of upward and downward concavity, and inflection points: g(x) 3x4 +4.x Pro):-I -2 16 3 a7 al 16 min(-1,-1) y " 30+24K: 12x(3x+2) t ip. (oo) 2 3 3. Find the equation of the tangent line to...
Above is a graph of y = f(t) Find; 1) g'(4) = 2) g''(4) = 6 5 4 3 2 1 2 -1 0 2 3 4 01 6 1 -21 Let gla) = * s(v) dt and use the graph to answer the following. Show your 0 reasoning
Question 7 14 Let f be a twice differentiable function, and let f(6) = 7, f'(6)=0, and f" (6) = 0. Which statement must be true about the graph of f? (6,7) is a local minimum point (6,7) is a local maximum point (6,7) is a global maximum point There's not enough information to tell. (6,7) is a point of inflection (6,7) is a global minimum point Question 5 14.3 pts Let f be a twice differentiable function. y С...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
Let if x<o if o sxs1 <xs 2 f(x) = O NO 2 - X lif O VIVA x and g(x) = f(t) dt JO (a) Find an expression for g(x) similar to the one for f(x). if x < 0 if o sxs 1 g(x) = 3 if 1 < x 2 if x > 2 (6) Sketch the graph of f. Sketch the graph of g. (c) Where is differentiable? (Enter your answer using interval notation.) Where is...