Question

Let f(x) be a polynomial function such that f(-5)=-2, f'(-5)=0, and f''(-5)=6. Classify the point (-5,-2).

Answer 1

a) intercept
b) inflection point
c) local minimum
d) local maximum
e) none of the above

Answer 2

First derivative zero means a critical point; second derivative positive means local minimum.

Answer 3

Right, I understand that. But as far as classifying the point (-5,-2)?

Answer 4

See, I thought that(-5,-2) was an intercept point. If x is -5, and f(-5) gives you -2, wouldn't that make -2 the u intercept? And thereby making (-5,-2) intercept points?

Answer 5

*y intercept I meant

Answer 6

Well the slope at that point is 0. So this tells that the tangent line to the curve that hits this point is a horizontal line.

The y-intercept is when x=0 tho

Answer 7

Well, the value of the function at x=-5 is y=-2. The other info means at that x value, the function has a local minimum.

Answer 8

Oh, yes, that's right. Y int at x=0. Sorry bout that.

Answer 9

hmm, but if the first derivative is a horizontal line then the second derivative wouldn't have a value of 6. This is a tough question

Answer 10

Yeah, I got it wrong on my final exam. I'm a bit bummed about it.

Answer 11

The second derivative tells how the slope is changing. If the slope is increasing (as it will when the second derivative is positive) there will be a minimum value at the point where the first derivative is zero.

Answer 12

Well, I think Animal is saying it is Local Min. Right, Animal? I don't have the correct answer, just my wrong answer.

Answer 13

Yeah. Local minimum is correct.

Answer 14

Intercept. It's not that one.

Answer 15

So because -5 is a local minimum, that classifies the entire point (-5,-2) as a local minimum?

Answer 16

The local minimum happens at x=-5; the value of the function at that point is y=-2. So, you might say the function has a local minimum at x=-5, or the local minimum value of the function is -2 in the neighborhood of x=-5.

Answer 17

Ok, that makes sense. Thanks for clearing it up.

Answer 18

No sweat. Do math every day.