Finding an Equation of a Tangent Line In Exercises43–46, find an equation of the tangent line to the graph of f atthe given point.43. f (x) = (x + 2)(x2 + 5), (−1, 6)
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Finding an Equation of a Tangent Line In Exercises
43–46, find an equation of the tangent line to the graph of f at
the given point.
43. f (x) = (x + 2)(x2 + 5), (−1, 6)
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- Finding a Derivative In Exercises 13–32, findthe derivative of the function. y = 5(2 − x3)4Find the natural domain and graph the functions in Exercises 15–20.15. ƒ(x) = 5 - 2x 16. ƒ(x) = 1 - 2x - x217. g(x) = sqrt( | x | ) 18. g(x) = sqrt(-x)19. F(t) = t/ | t | 20. G(t) = 1/ | t |Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\frac{1}{x-2}
- Using the definition, calculate the derivatives of the functions in Exercises 1–6. Then find the values of the derivatives as specified. 1. ƒ(x) = 4 - x2; ƒ′(-3), ƒ′(0), ƒ′(1) 2. F(x) = (x - 1)2 + 1; F′(-1), F′(0), F′(2) 3. g(t) = 1 /t2 ; g′(-1), g′(2), g′(sqrt(3)) 4. k(z) = (1 - z )/2z ; k′(-1), k′(1), k′(sqrt(2)) 5. p(u) = sqrt(3u) ; p′(1), p′(3), p′(2/3) 6. r (s) = sqrt(2s + 1) ; r′(0), r′(1), r′(1/2)In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)Exercise(7) 1.Find the intervals (Isolate the roots) of the equation f(x) = x - x - 1
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!Write a function that models the distance D from a point on the line y = 3 x - 10 to the point (0,0) (as a function of x). D(x) = The point on the line that is closest to (0, 0) is ) (numerical answers)Ron Larson - Calculus 11th Edition Chp 3.3 - Increasing and Decreasing functions and the first derivative test. Please show all work and explain steps, thank you!
- estion 1 If f'(x)=7x x-4 and f(4)= - 5, then what is f(5)? Moving to the next question prevents changes to this answTrue or false? Explain. If g (x)=x, then g x)=/x.Quantity vs. Rate-of-Change The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(x), million senior citizens, where x is the number of years after 2000. N(x) = 0.03x2 + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= --select units-- O gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through 2030. Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will…