2007-01-20 06:56:14 · 4 answers · asked by Belinda E 1 in Science & Mathematics ➔ Mathematics
x = 0.75
2007-01-20 07:13:07 · answer #1 · answered by Diapason45 7 · 0⤊ 0⤋
f(x) = y = 2 + 3x - (5 - x)²
f ` (x) = 3 + 2(5 - x) = 0 for stationary values
2(5 - x) = -3
5 - x = -3/2
x = 5 + 3/2 = 13/2
f(13/2) = 2 + 3 x 13/2 - (5 -13/2)²
f(13/2) = 2 + 39/2 - 9/4 = 8/4 + 78/4 - 9/4 = 77/4
Thus (13/2,77/4) is a turning point
Now f ` (x) = 3 + 10 - 2x
f " (x) = - 2 is negative (gives a Max turning point)
f "(13/2) = - 2
f (13/2) = 2 + 39/2 - (5 -13/2)²
= 2 + 39/2 - 9/4 = 8/4 + 78/4 - 9/4 = 77/4
Thus (13/2, 77/4) is a maximum turning point
2007-01-20 08:05:43 · answer #2 · answered by Como 7 · 0⤊ 0⤋
y = 2 + 3x - (5-x)^2
y = 2 + 3x - 25 + 10x - x^2
y = -x^2 + 13x - 23
Stationary points => gradient = y' = 0
y' = -2x + 13 = 0 => x = 13/2 = 6.5
When x=6.5, y = 2 + 3(6.5) - (5-6.5)^2 = 19.25
Stationary point = (6.5, 19.25)
2007-01-20 08:06:16 · answer #3 · answered by Kemmy 6 · 0⤊ 0⤋
Sorry, dont speak Geekese
2007-01-20 07:05:12 · answer #4 · answered by Northern Spriggan 6 · 0⤊ 2⤋