Question

Points of inflection please help! :)

Answer 1

Set the second derivative equal to zero, and solve for X

Answer 2

Find the x coordinate of each of the points of inflection of the graph f. Justify your answer.

Answer 3

I don't even know where to start! Please help. :)

Answer 4

That graph is the derivative graph.
So plan out:
You don't know f(x) [off hand]
You know f'(x)
And you're trying to find where the second derivative, f''(x), = 0.

Okay, think it out for a second...
What does f ' (x) mean if you were given a regular f(x) graph? The slope!
So look where the slope of the f ' (x) graph equals zero!

Seems like to me, the slope for the graph provided is Zero at (2,0) and (4,-2.5).

Let's think a bit logically for that...
Based on the f ' (x) graph given, we see that from -2 -> 2, the graph decreases a lot but starts to slowly round off.
We see that from 2 -> 4, the graph starts to go back to more and more negative, so it starts to go downward faster, and faster.
We see that from 4 -> 5, the graph starts to slow down, and round off a little until it hits x=5.
From x = 5, the graph starts to go positive!

(2,0) and (4,-2.5) are points of inflection.

Answer 5

Wow thank you so much! Why is it zero at (4, -2.5)?

Answer 6

Because the slope at that point is zero...
Remember, if you can sit on a slope without sliding off, then the slope equals zero!

Answer 7

Oh! That makes sense! Can you please help me with another question related to this graph? I will make another post so I can give you another medal. :)

Answer 8

Post it here if it's easier

Answer 9

Okay, find the x-value where f attains its absolute minimum and maximum value on the closed interval from x = -2 to x = 6. Justify your answer.

Answer 10

Also, what the the equation f the line tangent to the graph of a function h at x = 3 be?

Answer 11

Based on what I said about how the graph behaves...
Absolute minimum will occur when the graph goes so far down, it stops, and then starts going up.
The absolute maximum will occur when the graph goes so far up, and then it stops, and then starts going up.
So let's see the graph.



It goes really, really negative, and then starts to round off, and then goes even more negative! From -2 to 2, it goes very negative to a complete 0-slope, and then it starts to go more and more negative until it hits a complete 0 slope at x=5. Your absolute minimum must be at x=5!

It starts to go upward, higher and higher, until it hits x = 6.
Compare the start to the end.
You know that f(3) = 10. So everything before that must be higher than it because it has to constantly decrease until it hits 10 at x=3.
So I'm going to say that the beginning of the graph is where the absolute maximum is, and the absolute minimum will be at x=5.

Answer 12

Why x = 5? Isn't (4, -2.5) the lowest point on the graph?

Answer 13

I'll draw out the original function for you so it'll be easier to see everything.

Answer 14

Okay. :)