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4 years ago

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

express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

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8 0

1 year ago

PLZ HELP ASAP DUE RN

matrenka [14]

Answer:

The first and third options are correct so choose both

Step-by-step explanation:

4 0

2 years ago

A provider order has been received for a dobutamine (dobutrex®) drip at 7 mcg/kg/min. the patient's weight is 220 lbs. how many

Liula [17]

To figure this out you first need to determine how many kg there are in 220 lbs. 1 lb equals 0.454 kg, so 220 lbs= 99.88 kg.

It states that a patient receives 7mcg per kg per minute, so the patient will receive 7 x 99.88=699.16 mcg per minute.

You need to convert this to a number of mcg per hour, so multiply the amount by 60 to get 41949.6 mcg per hour.

4 0

3 years ago

PLEASE HELP ME ASAP!!! (DUE TOMORROW!!) Please help me with 9, 10, and 12!!!!!!!!!!

mina [271]

9.B

10.C

12.B

12. You have to do the circumference of the circle and then divide it by 2.

10. 7^2 is not 14 it is 49 because 7*7 is 49.

4 0

3 years ago

Express 5/4 as a mixed number and show the work

SCORPION-xisa [38]

Answer:

5/4 as a mixed number = 1 $\frac{1}{4}$

5 0

4 years ago