1) Let f(3) = 22 (Figure 24). Verify the following: 2-1 (a) f(0) is a local...
Show ALL work to receive rating. Thanks! 1. Let f(x) = -4x^3+6x^2 a) Where is f(x) increasing/decreasing? Make a sign chart. b) Classify the critical points as local max, local min, or neither. c) Where is f(x) concave up/concave down? Does it have any points of inflection? d) Use the information above to sketch the curve. Note that f(1/2) = 1. Be sure your graph includes the x and y intercepts if they exist.
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
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) = 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
For easy reference, f(z)- e- and its derivatives ()-2r(r-1)e 2r(r-1) 4r -8r +2 (x)-e(Az-8r+2)- and (c) Find lim (3) What is the horizontal asymptote? (d) Find the local max, local min, and/or inflection points, if they exist. You may use decimals (round to three decimal places) for your answers. (3) (e) Sketch the graph of f. Clearly label or state the points corresponding to the inter- cepts, asymptotes, local maxima and minima, and inflection points (if they exist). (6) 2...
True of False (dont need to solve) _____According to the L’hospital’s rule, lim(x-->a) f(x)/g(x)= L if f'(x)/g'(x)=L _____ A monotonically increasing function cannot have a max or min in a closed interval [a, b] because f’(x) >0 for all x in (a, b). _____ For x>10, the ratio ln(x)/sqrt(x-10) approaches 0 as x --> infinity . _____ lim(x-->infinity) (3x^3 +12x^2 -8x +1)/(x^2 + 2)(3x-1) =3 _____ _____ x = -1 is an asymptote of y= 1/(sqrt(x+1)) _____ _____ y=0 is...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
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...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
7. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I spilled my tea on the graph of f(x). The coffee dissolved the ink as shown. Please redraw the graph for me using the graph of f(x). (Hint: Graph f"(x) to determine the concavity of the original graph.) Be sure to indicate important features like relative max and min, points of inflection, increasing and decreasing intervals, and intervals where the graph is concave up...
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...