2) f(x) = 2- 1 Domain Range Zeros x-intercept y-intercept Continuity Increase Interval Decrease Interval 2 -5 -1 Maximum x = -20, find f (x) x = 4, find f(x) Minimum -1 -2 -3 as x → -00 as x → +0o 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?On the interval 2 < x < 4, there is a relative… •maximum •minimum •increasing •decreasing •constantFind 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)
- What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local minimum at x = 3? b. a local minimum at x = 4 and a point of inflection at x = 1?What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum at x = 3?Does ƒ(x) = (7 + x)(11 - 3x)^(1/3) have an absolute minimum value? An absolute maximum? If so, find them or give reasons why they fail to exist. List all critical points of ƒ.
- On the interval -2 < x < 1, the function is… •maximum •minimum •increasing •decreasing •constantWhat is the absolute minimum value of p(x)=2x^2+x+2 over [−1,3]?If 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=____
- Does x=3 belong to a local maximum or a local minimum? Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local minimum?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?Determine the critical value(s) of y = -8x^2+ 12x + 3 and state if it is relative minimum or relative maximum.