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Oh boy I can do this problem! =D

y = x² + 8x - 9

We need to take the derivative of this. That will tell us the slope of the graph of this function at any point. Take the derivative using the power rule.

y' = 2x + 8

Set y' = 0 to find all the places where the slope of x² + 8x - 9 is zero.

0 = 2x + 8

-8 = 2x

-4 = x

So when x is -4, the slope of x² + 8x - 9 is zero. That means it is either a maximum, minimum, or inflection point. To figure out which one, take the second derivative.

y''= 2

Since y'' is positive when x is -4, that means the graph is concave up, which means x = -4 is the minimum.