Question

Show that y = x^2 - 3x + 7 is concave up for all values of x.

Answer 1

It is concave up if its second derivative is always positive, i.e. y ' ' > 0

y' = 2x - 3
y ' ' = 2

So y ' ' is positive always, hence, always concave up.

Answer 2

What would I need to do after that to show that it is always positive? A table of values?

Answer 3

y ' ' = 2 means that the second derivative is a positive number called 2. That alone is sufficient!

Answer 4

I see. Thank you!

Answer 5

welcome.