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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

A.

13

B.

-13

C.

1

D.

-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