Question 32 $ider the Tunction de.by4001if x < 0300f(x) =-x +11200if x > 0100x +1X102030405060Sketch this graph and find all points where the graphis continuous but not differentiable.temperatureFigure 2.53 Enzyme activity as a function of temperature.30. Consider the function defined by0 ifx <034. In Example 7 we discussed how the extent of Arcticsea ice is modeled by the functionif 0 < x < 1f(x) =1if x > 1S(t) = 7.292 + 0.023t – 0.004t² million squarekilometersSketch this graph and find all points where the graphis continuous but not differentiable.where t is years after 1980. Use the definition of thederivative to compute S'(20). How does this valuecompare to S'(30) found in Example 7? What doesthis comparison suggest about the rate at whicharctic ice is being lost?Level 2 APPLIED AND THEORY PROBLEMS31. Abaseball is thrown upward and its height at time tin seconds is given by35. In 2010, W. B. Grant published an article aboutthe prevalence of multiple sclerosis in three U.S.communities and the role of vitamin D. The best-H(t) = 64t– 16t2 feeta. Find the velocity of the baseball after twofitting quadratic relationship to the data published inthis article, relating prevalence of multiple sclerosis(MS) to latitude (exposure to sunlight, hence vita-min D synthesis decreases with latitude) is shown inFigure 2.54. This quadratic function is given byseconds.b. Find the time at which the baseball hits theground.c. Find the velocity of the baseball when it hits theground.Р(x) — 499 — 30.8х + 0.5х? сases per 100,00032. A ball is thrown directly upward from the edge of acliff and travels in such a way that t seconds later, itswhere x is latitude.enzyme activity 2.6 Derivative at a Point18123.24.height above the ground at the base of the cliff isyH(t) = -16t? + 40t + 240.8feet.106a. Find the velocity of the ball after two seconds.b. When does the ball hit the ground, and what is itsimpact velocity?0.4-2-112 x-10.2c. When does the ball have a velocity of zero? Whatphysical interpretation should be given to thistime?-2E1.0 –0.50.51.033. If the data in Figure 2.53 represents a set of measure-ments relating enzyme activity to temperature indegrees Celsius, and the quadratic equation25. f(x) = |x - 2|26. f(x) = 2|x +1|if x < 1x – 3 ifx > 1(-2x27. Let f(x) =A(x) = 11.8 + 19.1 x – 0.2 x²a. Sketch the graph of f.provides a good fit to this data, then find A'(50) anddiscuss its meaning.b. Show that f is continuous, but not differentiable,at x = 1.28. Give an example of a function that is continuous on(-0, 0) but is not differentiable at x = 5.y%3|50029. Consider the function defined by4001if x < 0300-x +11|f(x) =200if x > 0100X +10 -102030405060Sketch this graph and find all points where the graphis continuous but not differentiable.temperatureFigure 2.53 Enzyme activity as a function of temperature.30. Consider the function defined by0 ifx <034. In Example 7 we discussed how the extent of Arcticif 0enzyme activity

Here the ball is thrown upwards from the edge of a cliff. The height of the ball from ground is…

height above the ground at the base of the cliff is H(t) = -16t2 + 40t +24 feet. a. Find the velocity of the ball after two seconds. b. When does the ball hit the ground, and what is its impact velocity? c. When does the ball have a velocity of zero? What physical interpretation should be given to this time?