Question

Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f (x) = x2 + 9x − 4 relative minimum
(x, y) =
relative maximum (x, y) =

please help me

Answer 1

To find relative extrema, you want to figure out when the derivative is 0, which represents a change in direction of your function.

Answer 2

So can you take the first derivative and solve for x when the derivative is 0?

Answer 3

oki so 2x+9 is the first derivitive

Answer 4

This is a parabolic function with positive first coefficient, so it has no upper bound (maximum does not exist). And has only one extremum(minimum) at the "top" of the function/ x=-4.5 y=-259/4.

Answer 5

SO THE MAXIMUM POINT would be (-4.5,-259/4)

Answer 6

i mean the minimum point

Answer 7

It is the only point where the derivative vanishes, and the second derivative is positive at this point, so it is the only extremumu and it is minimum

Answer 8

so thats the point right

Answer 9

Sorry I went away. You got the first derivative right. 2x + 9. And this is only 0 when x = -4.5. Now you can recognize whether this is a max or min any number of ways. You can just test a few y values around it or you can graph the function or whatever.

Answer 10

But I believe what they want you to do is take the second derivative and check what it is at that x point. So the second derivative is the derivative of 2x+9 which is just 2.

Answer 11

Which means that the function has positive 2nd derivative at x=-4.5, so it's concave up.

Answer 12

can you help me with the other question i just posted please

Answer 13

Surely.

Answer 14

thanx