Chapter 9, Problem 29RE

e3x-6-2, if x ≤ 2 f(x) = [2x - 5], if 2 3 x²-9, 2. Find f'(2), if it exists.

Differentiate the function. G'(q) = = G(q) = (6 + q−¹)²

The distance a biker has traveled after t seconds can be modeled by f(t) feet and f(50) = 64. f'(t) > 0, and f"(t) < 0. Which of the following is the correct interpretation of this information? The biker'sistance is increasing less and less. The biker's distance is increasing more and more. The biker's distance is decreasing less and less. O The biker's distance is decreasing more and more. O none of the above

_1 Which of the following is an exponential function? а) у - х b) f(x) = x² c) y = 22 d) f(x) = 2* _2 What does it imply when the graph of f(x) = a* is asymptotic to x axis? a) The graph's trend increases to the left of the y – axis. b) The graph's trend decreases to the left of the y – axis. c) The graph's trend decreases to the right of the y – axis. d) The graph's trend can either be that of a growth or decay function. _3 What will be the behavior of the graph of an exponential function if the y intercept is at (0, 2)? a) The graph follows an exponential growth. b) The graph follows an exponential decay. 4 The formula for the Richter rating of a quake is given by R - logQ. You have a seismograph set up at home and see that there was an event while you were out that had an intensity of Q = 989. A Richter rating of 4 or more means a moderate quake occurred. Which of the following is TRUĚ given the situation? a) The intensity of 989 is the result of a strong quake. b) The intensity of…

Paragraph Styles 4. Suppose that f(4)-2, g(4)-5, /(4-6, and g'(4)- 3. Find derivative h'(4) in (a) (a h(x) 3f +8g) (b) ho)-g) f(x) g (x) g(x) f)+g)

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If sales N(x) are expressed as a function of the amount a spent on advertising, then the dollar amount at which N' (x), the rate of change of sales, goes from increasing to decreasing is call the [Select] If d is that dollar amount, then (d, N(d)) is [Select] ✓ of N(x).

(part 1 of 4) Find the nth-derivative, f(n), of f(x) e2x+4. 1. f(n)(x) 2. f(n)(x) 4. f(n) (x) 5. f(n) (x) 1. T3(x) 3. f(n)(x) = — - ²x- n! e²x+4 2. T3(x) 3. T3(x) - = 6. T3(x) = = = = 6. f(n)(x) = n! e²x+4 = (part 2 of 4) Find the degree three Taylor polynomial T3 centered at x = 0 for f when f(x) In(3 – 4x). 2n2x+4 n! = n! 2ne2x+4 2ne²x+4 4 = In 3- col e²x+4 3x 5. T3(x) In 3 4 4. T3(x) = x ₁ -x + T 4 -X 3 8 4 In 3+x 3 9 8 4 =x + 3 4 8 3⁰⁰ ∞ 18 + =x² + 8 9 64 81 8 2 64 8 81 -x3 n3 64 81 3 64 81 23 32 81 تر 64 81

In Exercises 59-64, let f(x) = 2x – 5 %3D g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. 59. (fog)(0) 61. f-(1) 60. (go (0) 62. g-'(7) 64. f(g[h(1)]) 63. g(f[h(1)])