Please answer question number 12 parts A and B. a. The graph of the derivative of a function is given. From this graph determine the intervals in8.which the function increases and decreases. Justify your answer-5b. The graph of the 2nd derivative of a function is given. From this graph determine the intenelin which the function is concave up and concave down. Justify your answer,-31249. Consider the function h(x) = 14 + 4x3 –x*.a. Identify the critical points of the function.b. Determine the intervals on which the function increases and decreases.c. Classify the critical points as relative maximums, relative minimums or neither.d. Determine the intervals on which the function is concave up and concave down.e. Determine the inflection points of the function.f. Use the information from steps (a) – (e) to sketch the graph of the function.10. We want to construct a cylindrical can with a bottom but no top that will have a volume of 65 cubicinches. Determine the dimensions of the can that will minimize the amount of material needed toconstruct the can.11. Use Newton's Method to find the root of the given equation, accurate to three decimal places, that liesin the given interval: 2x3 – 9x² + 17x + 20 on [-1,1].12. Evaluate the following integrals:a. S(2x4 - Vx3 + x)dxb. (1-2x)(3+x)(1+x)5x13. Use the definition of the definite of a definite integral as the limit of a Riemann Sum to evaluateS(7 - 4x)dx. Verify your answer by using a formula from geometry.14. State the Fundamental Theorem of Calculus (both parts). Illustrate with an example15. Evaluate the following integrals: S V2x – x³ (4 – 6x²)dx. Draw a diagram and shade the regionwhose area is represented by the integral. Feel free to use technology to aid with graphing.GRAD

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Answered: 12. Evaluate the following integrals:…

Math

Algebra

12. Evaluate the following integrals: a. S(2x* - Vx3 + x)dx (1-2x)(3+x)(1+x) dr b. fa- 5x

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.4: Composition Of Functions

Problem 97SE: The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is...

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