Find the value of x at the minimum point of the curve y =...
Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1
13
-13
1
-1
Correct answer is A
y = x3 + x2 - x + 1
dydx = d(x3)dx + d(x2)dx - d(x)dx + d(1)dx
dydx = 3x2 + 2x - 1 = 0
dydx = 3x2 + 2x - 1
At the maximum point dydx = 0
3x2 + 2x - 1 = 0
(3x2 + 3x) - (x - 1) = 0
3x(x + 1) -1(x + 1) = 0
(3x - 1)(x + 1) = 0
therefore x = 13 or -1
For the maximum point
d2ydx2 < 0
d2ydx2 6x + 2
when x = 13
dx2dx2 = 6(13) + 2
= 2 + 2 = 4
d2ydx2 > o which is the minimum point
when x = -1
d2ydx2 = 6(-1) + 2
= -6 + 2 = -4
-4 < 0
therefore, d2ydx2 < 0
the minimum point is 1/3
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