question archive (a) Evaluate g(x) for x = 0, 3, 6, 9, 12, 15, and 18
(a) Evaluate g(x) for x = 0, 3, 6, 9, 12, 15, and 18
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(a) Evaluate g(x) for x = 0, 3, 6, 9, 12, 15, and 18.
| g(0) | = | |
| g(3) | = | |
| g(6) | = | |
| g(9) | = | |
| g(12) | = | |
| g(15) | = | |
| g(18) | = |
(b) Estimate g(21). (Use midpoint to get the most precise estimate.)
g(21) =
(c) Where does g have a maximum and a minimum value?
| minimum at x | = |
| maximum at x | = |
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(a)
g(0) = 0
g(3) = 1/2 * 3 *3 = 4.5.
g(6) = g(3) - g(3) = 0.
g(9) = g(6) - g(3) = - 4.5
g(12) = g(9) + g(3) = 0.
g(15) = g( 12) + 9 + g(3) = 13.5
g(18) = g(15) + g(3) + 6*3= 13.5 + 4.5 + 18 = 36.
(c)
g(x) is maximaum or minimum only if g ' x = 0.
which is when f(x) = 0. from the given definition.
hence f(x) = 0 when x = 3, 9,21.
g(3) = 4.5, g( 9)= -4.5
hence in case of minimum 9 is the answer while in the case of maximum 21 is the only answer
as it is greater than g(18).
