Exercises to be solved and broken downThe exercises are 6,29 33%P 5:35Asiacell lI..h Thomas Calculus_ Early Transcende... p4oIn Exercises 5–10, find an equation for the tangent to the curve at thegiven point. Then sketch the curve and tangent together.5. у %3D 4 — х2, (-1,3)6. у %3D (х — 1)? + 1, (1, 1)7. y = 2Vx, (1, 2)8. у 31(-1, 1)9. у %3Dх, (-2, -8)10. y = . (-2.-)2, -In Exercises 11–18, find the slope of the function's graph at the givenpoint. Then find an equation for the line tangent to the graph there.11. f(x) = x² + 1, (2, 5)12. f(x) — х — 2х?, (1,—1)8(2, 2)х13. g(x)(3, 3)14. g(x) =x – 2'15. h(t) = t°, (2, 8)16. h(t) = t³ + 3t, (1, 4)17. f(x) = Vx, (4, 2)18. f(x) = Vx + 1, (8, 3)In Exercises 19–22, find the slope of the curve at the point indicated.19. у %3D 5х —3x2,x = 120. у 3D х3 — 2х + 7, х % -2121. у 322. у %3x – 1x = 3x = 0х — 1°x + 1' 33%P 5:36Asiacell lI..Thomas Calculus_ Early Transcende... piInterpreting Derivative Values23. Growth of yeast cells In a controlled laboratory experiment,yeast cells are grown in an automated cell culture system thatcounts the number P of cells present at hourly intervals. The num-ber after t hours is shown in the accompanying figure.edge to make a roughper x-unit) at the pointsP250200150100502 3 4 5 6 7a. Explain what is meant by the derivative P'(5). What are itsunits?b. Which is larger, P'(2) or P'(3)? Give a reason for youranswer.c. The quadratic curve capturing the trend of the data points(see Section 1.4) is given by P(t) = 6.10r2 – 9.281 + 16.43.Find the instantaneous rate of growth when t = 5 hours.24. Effectiveness of a drug On a scale from 0 to 1, the effective-ness E of a pain-killing drug t hours after entering the blood-stream is displayed in the accompanying figure.1.00.80.60.40.2ngent to the curve at thetogether.- 1)? + 1, (1, 1)145a. At what times does the effectiveness appear to be increasing?What is true about the derivative at those times?- (-1, 1)b. At what time would you estimate that the drug reaches its- (-2-)maximum effectiveness? What is true about the derivative at-2,-that time? What is true about the derivative as time increasesin the 1 hour before your estimated time?ion's graph at the givennt to the graph there.At what points do the graphs of the functions in Exercises 25 and 26have horizontal tangents?х — 2х?, (1,—1)25. f(x) = x² + 4x - 127. Find equations of all lines having slope -1 that are tangent to the26. g(x) = x – 3x8(2, 2)curve y = 1/(x - 1).3 + 31, (1, 4)Vx + 1, (8, 3)28. Find an equation of the straight line having slope 1/4 that is tan-gent to the curve y = Vx.e at the point indicated.Rates of Change29. Object dropped from a towertop of a 100-m-high tower. Its height above ground after t sec is100 – 4.91? m. How fast is it falling 2 sec after it is dropped?- 2x + 7, x = -2An object is dropped from the- 1X = 0+ 1°

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tain we and tangent together. 6. у %3D (х — 1)? + 1, (1, 1) 1