On what interval is the function f(x)=x^3-4x^2+5x concave upward?

1 answer:

3 0

Calculus 1?

To find concavity you must take the second derivative.

As you would to find your local maximums and minimums (critical points) in the first derivative by setting y' = 0, to find points of inflection you set acceleration, y" = 0.

Now that you know where the point in which the function is neither concave up or concave down (at the points of inflection) plug x-values between them into the second derivative for x. If y" is positive between those particular points will be concave up and if y" is negative it will be concave down between that interval.

For a better understanding you might find a good video on Youtube explaining this if you search "Points of Inflections" or "Concavity of a function".

Cheers.

You might be interested in

¼c+3d when c and d=7

-Dominant- [34]

Answer:

22.75

Step-by-step explanation:

you substitute the 7 in for c and d. Following PEMDAS, you would then do (1/4) multiplied by 7 and 3 times 7. add those 2 together and you get 22.75 :)

8 0

3 years ago

Solve -2/3x > 8 or -2/3x < 4.

vekshin1

<h3>Answer: Choice C</h3>

{x | x < -12 or x > -6}

=========================================================

Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to <u>choice C</u> as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

8 0

2 years ago

(x+6)(x-2)(x-1)=60 write a polynomial

enot [183]

For this case what you should do is:
1) Multiplication of terms within parentheses correctly.
2) Rewrite the expression respecting power properties.
3) Add or subtract terms of equal power.
Note: See attached image.
Answer:
x ^ 3 + 3x ^ 2 -16x - 48 = 0