How do you do these two questions?

Mathematics

1 answer:

Mice21 [21]3 years ago

4 0

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.

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