Question

CALCULUS:

Can you help me out with this?
http://screencast.com/t/M74UKjB9B5

Answer 1

@e.mccormick @Mertsj @modphysnoob @timo86m @Meepi @ganeshie8

Answer 2

Hey mertsj!

Answer 3

Find the first derivative.

Answer 4

If the first derivative is >0, the function is increasing.
If the first derivative is <0, the function is decreasing.

Answer 5

2x-3

Answer 6

but how can I know the value if I dont know x

Answer 7

Ok, when the function is INCREASING, the DERIVATIVE will be POSITIVE
so solve 2x-3>0
And when DECREASING, the DERIVATIVE is NEGATIVE
so solve 2x-3<0

Answer 8

Solve 2x-3>0

Answer 9

Solve 2x-3<0

Answer 10

3<3/2 x>3/2 what now?

Answer 11

x<3/2 ****

Answer 12

when CONCAVE UP, the SECOND DERIVATIVE will be POSITIVE
and CONCAVE DOWN, the SECOND DERIVATIVE is NEGATIVE

Answer 13

Thanks!! I see!

Answer 14

How about the inflection point??

Answer 15

@apple_pi @Mertsj

Answer 16

Points of inflection are points where f(x) changes concavity. For example if f ''(x) > 0 for x < a, and f ''(x) < 0 for x > a, then (a, f(a)) is a point of inflection.

Answer 17

Your function is a parabola which opens upward, thus it is always concave up, hence there is no change in concavity. Therefore there is no point of inflection.

Answer 18

So does number 16 have a point of inflection ?

Answer 19

problem #16

Answer 20

You tell me? What degree polynomial is the function in question 16?

Answer 21

The degree of the polynomial function is the highest exponent of x. So answer my question please because I'm here to teach you, not just give you the answers.

Answer 22

2nd degree

Answer 23

That's right so then it's the same as question 15 except that this time the coefficient of x² is negative. What does this imply, when the leading coefficient of a quadratic polynomial function is negative?

Answer 24

Hint: In question 15, the leading coefficient (the coefficient of the term with the highest power of x) was positive, which implied that the parabola's direction of opening was upward. Hence what is the direction of opening of the parabola in question 16?

Answer 25

im confused. cant you just tell me the answer and the reason behind it please

Answer 26

im new to calculus i dont understand these terms so well

Answer 27

In question 15, x² was positive so the parabola opened upward. In question 16, do we have positive x² or negative x² ? I'm a teacher, and therefore it goes against everything I stand for, to just give you the answer. So please answer my questions. Don't worry about being wrong, because that is part of learning.

Answer 28

its negative?

Answer 29

Right? So what does that say about the parabola's concavity (direction of opening)?

Answer 30

it goes all the way down? no change?

Answer 31

If you mean it is always concave down (direction of opening is downward), then BRAVO! Now how can we prove with elementary Calculus that it is always concave down?

Answer 32

uhm What do you mean to prove? :/

Answer 33

Using the methods of calculus, how would you arrive at the conclusion that the function in question 16, y = 5 - 4x - x² is concave down for all x (always concave down)?

Answer 34

Hint: Would you draw that conclusion from the first derivative or the second derivative?

Answer 35

Hint: The first derivative helps you locate the intervals of increase/decrease, and critical points (points where the local extrema may be). The second derivative helps you find the intervals of concavity and possible points of inflection.

Answer 36

If y = 5 - 4x - x². y'' = ?

Answer 37

I'll be back in a few minutes. I'll be anticipating a response from you, while I'm away.

Answer 38

\[y'' = \frac{ d ^{2}y }{ dx ^{2} }= f''(x)= D _{x}^{2}y=...\]These are symbols for the second derivative. Do you know how to find the second derivative? Yes or No? There's not much communication, if I'm the only talking. Please say something.