Question

Math question

Answer 1

@jim_thompson5910 Would it be C or D?

Answer 2

\(f(x)=(-x+4)^5+1\)

like this?

Answer 3

Yes

Answer 4

I haven't seen people do this without differentiation, really, but I guess that the concept is the same just that you won't be able to use calculus as the tool.

In the world of calculus there are 3 cases of critial points:

1) When f'(x) (the function's derivative is undefined)
2) When f'(x)=0 (the function's derivative is equal to zero)
3) If closed interval is given, then the endpoints of closed interval are critical points.

I will translate this into our problem.

1) When the function doesn't have a slope at a certain point
--> but this can't be true by a polynomial (which it is in our case)

2) When the slope of the function is zero (yes, that is a possiblity)
--> if you were to graph the function those are the turning points - or think of those points as such that they have a horizontal tangent.

for #3,
--> no, because no interval is given.

Answer 5

Also an odd-power polynomial will go into neg and pos infinity on its ends, thus no maximum or minimum present.

Answer 6

Points of inflection is when the second derivative of the function is zero, or in other words, when the function changes its "concavity" (from concave up to concave down)

or when the slope stops increases and starts to decreases (or vice versa) , then the point at which it changes from increase to decrease (or vice versa) -- that is the inflection point.

Answer 7

So it is D?

Answer 8

should I give you an example of inflection point without calculus?

Answer 9

Inflection point actually are present, I believe

Answer 10

No, it's ok. It is C, point of inflection. Thank you!