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Determine intervals of increasing and decreasing. Show your work using a First Derivative Test. Identify the function’s local and absolute extreme values, if any, saying where they occur.f(x) = -x3- 1.5×2 + 36x – 2

Consider a continuous function, f, whose domain is all real numbers. If f(4) = 14 and the derivative at 4 is -3, also the second derivative is positive for all x, Could f(6) = 8 Explain

If f(x) has a positive derivative over (- ∞ , -7) and (-7, 2) and a negative derivative over (2, ∞ ), and a derivative equal to 0 at x = -7, what can you say about x = -7? what can you say about x = 2? (Think in terms of CV, max/min, inflection points, etc. Support your answer.)

Solve the problem.The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h, in feet, was approximated by the functionh = -0.002d2 + 0.7d + 6.2.Find the relative maximum of the function.

Provide an appropriate response.Find the absolute maximum and minimum values of f(x) = 2x – ex on [0, 1].

An insect is crawling along a horizontal line. On what intervals is the insect’s velocity negative? Where is the insect accelerating? Discuss the insect’s displacement vs distance.

For an artificial tendon requiring large reversible deformation at low loads, which biomaterial class is MOST appropriate? A. Ceramic biomaterials with high compressive strengthB. Metallic biomaterials with excellent fatigue propertiesC. Polymeric biomaterials with elastic chain motionD. Composite biomaterials reinforced with ceramic phases

 II Corinthians   But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly about my weaknesses, so that Christ’s power may rest on II Corinthians 12:9  

Bone is classified as a composite biomaterial primarily because it: A. Is completely inorganic and crystalline in natureB. Contains ceramic and polymeric componentsC. Exhibits metallic bonding under physiological loadD. Forms through artificial processing techniques

There was no such thing as “then” when there was no time. Augustine, Confessions, Book XI, Chapter 13, Paragraph 15