Advanced Placement (AP), 06.01.2023 03:50 drma1084

AP Algebra PLS HELP
f(x)=-1/2x+50 explain what the graph of the function represents

Answers

Answer from: Quest

Repeat the accusation

Answer from: Quest

Unconscious and the importance of childhoodhoped this can i get brainliest

Answer from: Quest

correct answer for apex users would be /opportunities for growth/

Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Other questions on the subject: Advanced Placement (AP)

Advanced Placement (AP), 24.06.2019 11:00, wtwbegay

The subject option isn't available. the topic is earth science!suppose you are a city engineer whose job it is to explore how to use more renewable energy in your locality. 1. consider the resources in your city and select one of the following: - hydropower -solar power -wind power -geothermal power 2. prepare a pamphlet or multimedia presentation to convince a committee of citizens and local leaders that the renewable energy source you have selected is best for you locality. in your pamphlet or presentation include: - a discussion of the renewable energy source that is best for your town and why -a discussion of the advantages and disadvantages of this energy source -a discussion of why you think your city should use more of this energy source -how the use of renewable energy will impact your city -pictures and/or charts and tables to strengthen your arguments

Answers: 1

continue

Advanced Placement (AP), 24.06.2019 16:00, christeinberg1

Choose the description that best matches each word. write the correct letter in the blank. 1. ostinato a. large, extended composition for chorus and orchestra 2. atonality b. full orchestra 3. musicology c. festive, march-like opening to a play or “semi-opera” 4. concerto d. small group of solo instruments 5. minimalism e. music contrasting a full orchestra and solo instruments 6. art song f. music played under the action to influence the mood 7. strophic form g. a vocal song focusing on artistic expression 8. incidental h. each stanza of a poem is set to the same music 9. oratorio i. repeated musical pattern that provides unity to a piece 10. dissonance j. steady beat; simple harmonies; short, repetitive melody 11. concertino k. harsh, unstable sounding of pitches; harmonic tension 12. tutti l. all 12 tones of chromatic scale, no tonal center 13. entrada m. the historical and scientific study of music

Answers: 3

continue

Advanced Placement (AP), 24.06.2019 17:30, kat9940

Which tip applies to the aspire test and psat equally

Answers: 1

continue

Advanced Placement (AP), 25.06.2019 02:00, bougiehairstudios

What inspired to create the film gladiator

Answers: 1

continue

You know the right answer?

AP Algebra PLS HELP
f(x)=-1/2x+50 explain what the graph of the function represents...