1) f(x) = -(x – 3)² + 3 Domain Range Zeros x-intercept y-intercept Continuity Increase Interval Decrease Interval Maximum Minimum x=-2, find f(x) x= 6, find f(x) as x -00 as x- +0 Vertical Asymptote Horizontal Asymptote
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- 2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?find the maximum and minimum values of the func- tion on the given interval y=2x2−4x+2, [0,3]5x−12/x^2−x−42 has vertical asymptote(s) at x=
- 9. A rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given that the available materials for the fence are good for 24m, what dimensions will produce a maximum area for the fence? What is the equation that will give us the function's critical point/s1. Find the absolute maximum and minimum values of f(x)=10x(2-lnx) on [1,e^2] 2. Find the limil. Uisng L'Hopital's Rule : lim x arrow 0 sin^2(3x)/4xIf the above graph is the graph of f′(x), then f(x) has a local maximum at x=___, a local minimum at x=____ and a critical point that is neither a local maximum nor a local minimum at x=____
- In the function: f(x)=(12−3x)e^x What are the critical numbers of the function? When is the function increasing and decreasing in interval notation? What are the x-coordinates of all local minimums and maximums?A rectangle is inscribed in the region bounded by the graph of y= e1-2x^2 and have one of its side lie on the x-axis. What are the dimensions of such a rectangle with the largest possible area?A rectangle is inscribed in the region bounded by the graph of y= e1-2x^2 and have one of its side lies on the x-axis. What are the dimensions of such a rectangle with the largest possible area?
- Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11)Use limits to determine the equations for all horizontal asymptote. y = (1 - x2)/( x2 + 1)False. For example, the maximum off (x) = x 2 + 1 on [l, 2] is 5, occurring at x = 2, but f' (2) # 0. (c) True (d) False. For example, the function f (x) = 2x 2 - x 3 has a single local minimum on [-1, 3], at x = 0, but the absolute minimum on [ -1, 3] occurs at the endpoint x = 3.