Question

How do you do these two questions?

Answer 1

Answer:

a) d²y/dx² = ½ x + y − ½

b) Relative minimum

Step-by-step explanation:

a) Take the derivative with respect to x.

dy/dx = ½ x + y − 1

d²y/dx² = ½ + dy/dx

d²y/dx² = ½ + (½ x + y − 1)

d²y/dx² = ½ x + y − ½

b) At (0, 1), the first and second derivatives are:

dy/dx = ½ (0) + (1) − 1

dy/dx = 0

d²y/dx² = ½ (0) + (1) − ½

d²y/dx² = ½

The first derivative is 0, and the second derivative is positive (concave up).  Therefore, the point is a relative minimum.