Question

[9.01] Determine whether the graph of y = x2 + 2x − 8 has a maximum or minimum point, then find the maximum or minimum value.

Answer 1

So, there are maximum and minimum points where the tangent line of a graph = 0. Tangent lines are found by finding the derivative. If we want a maximum or minimum, then we want a tangent line = 0. So I'll take the derivative of the function and find all x values for which y'(x) = 0
The derivative of x^2 + 2x - 8 would be 2x + 2
Setting 2x+2 = 0 leaves me with x equal to -1. So I know I have a tangent line equal to 0 at x = -1. To determine if this is a minimum or maximum, you'll do the first derivative test. If the derivative of a function at a point is less than 0, then the function is decreasing at that point. If the derivative at an x value is greater than 0, the function is increasing at that point. Essentially, we want to test each side of x = -1 and see what the function is doing on each side. So if the derivative is 2x+2, I'll choose x = -2 to check the behavior on the left of the critical point. When x = -2, the derivative = -2, meaning the function is decreasing to the left of x = -1. Testing a point to the right of -1 now. If I choose 0, the derivative will then = 2, meaning the function is increasing at that point. Now, when a function shifts from decreasing to increasing at a point, the function has a minimum at that point. So you would have a minimum at x = -1. And to get the y-value, just plug x = -1 into the original equation. When x = -1, y = (-1)^2 + 2(-1) - 8, which = -9, so your minimum is at the point (-1, -9). I know that was a long explanation, so gloss it over and see what ya think.

Answer 2

o_0 ok then... thank you!!!!

Answer 3

Yeah, np. See if it makes sense, though, first xD

Answer 4

haha ok thanks again

Answer 5

Mhm ^_^