Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) S49 - x2 F(x) = 2x - 3 if -7 Sx<0 %3D if 0sxs7 absolute maximum absolute minimum -3 local maximum DNE local minimum
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) S49 - x2 F(x) = 2x - 3 if -7 Sx<0 %3D if 0sxs7 absolute maximum absolute minimum -3 local maximum DNE local minimum
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) S49 - x2 F(x) = 2x - 3 if -7 Sx<0 %3D if 0sxs7 absolute maximum absolute minimum -3 local maximum DNE local minimum
Find the absolute maximum and the local minimum of the piecewise function given above.
Transcribed Image Text:Please try again. Use the first and second derivatives to find the intervals where the function is increasing or decreasing, and where the function is concave up or down. Using this
general information and with a few plotted points, you can obtain a sketch of the function. Keep in mind that when plotting a piecewise defined function, you should consider each
piece separately. Alternatively for this specific problem, you may use your knowledge about the graphs of lines and transformations of x².
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.)
S49 – x2
f(x) =
if -7 <x < 0
2x - 3
if 0 <x<7
absolute maximum
absolute minimum
-3
local maximum
DNE
local minimum
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Please try again. Use the first and second derivatives to find the intervals where the function is increasing or decreasing, and where the function is concave up or down. Using this
igeneral information and with a few plotted points, you can obtain a sketch of the function. Keep in mind that when plotting a piecewise defined function, you should consider each piece
separately. Alternatively for this specific problem, you may use your knowledge about the graphs of lines and transformations of x2.
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Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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