Matching In Exercises 5-8, match the Taylor polynomial approximation of the function
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Calculus
- The figure below shows the graph of the polynomial function f. For which value of x is it true that f"(x) < f'(x) < f (x)? а. b. b С. d. d е. e Graph of farrow_forwardf(0) = 1, f(1) = 3, f(3) = 55, find the unique polynomial of degree 2arrow_forwardSketch a cubic function (third degree polynomial function) y = p(x) where p(x) > 0 on the intervals (-∞0, 2) and (4,6). Then determine a formula for your function. Sketch: Formula: p(x)=arrow_forward
- Runge's function is written as f (x) = 1 1+ 25x² Generate five equidistantly spaced values of this function over the interval: [-1, 1]. Fit these data with (a) a fourth-order polynomial, (b) a linear spline, and (c) a quadratic spline. Present your results graphically.arrow_forwardLet f(x) =x/x + 1 and g(x) =2/x . (a) Find a formula for the composition (f . g)(x). Express the composition in simplied form, i.e. not as a complex fraction. (b) Find the domain of the composite function (f . g)(x)arrow_forwardID: A Name: 6. The table below gives velocity data for a rocket shortly after liftoff. Time (s Velocity (m/s) 0 0 10 63 15 86 20 110 30 203 358 55 546 70 963 90 Determine which of the following cubic polynomials best models the velocity of the rocket for the time interval te [0, 90]- v(t) = 0.001101t - 0.06979 t 8.158t - 10.19 2 3 a. 2 + 8.171t - 6.609 3 - 0.1143 t b. v(t)=0.001589t 2 v(t) 0.000205t 0.09749 t 2.704t + 16.31 с. 2 + 3 d. v(t)=0.001028t - 0.07601t 7.954t - 7.364 2 6.585t - 5.895 3 v(t)= 0.000331t 0.005495 t Io I е. 7. A cubic function is a polynomial of degree 3; that is, it has the form 2 3 + bx + CX + d f(x) ax 1 + 2bx tC 3ах2arrow_forward
- 1) Use the key features to sketch the polynomial function. End Behavior: As x → -0o, f(x) → -0 As x → co, f(x) → o Intercepts: x-intercepts: (2, 0), (-2, 0), (5, 0) -2- y-intercept: (0, 7) -3 -2 -2 Increasing/Decreasing: The intervals on which g decreases: (1, 3) -5- The interval on which g increases: (-∞, 1), (3, ∞) -7- Minimum/Maximum: A relative minimum occurs at (3, -4) A relative maximum occurs at (-1, 9)arrow_forwardii) Now let f (x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For example, the polynomial above is of order 5, since it has highest non-zero coefficient c5 = 2. Show that f(n+1)(x) = 0arrow_forwardDerive a first order formula to approximate f"(x) by using f (x - h), f(x) and f(x + 3h). Write the scheme explicitly and find the order of approximation. A.) f"(x) = S(x-n)+2f(x+3h)-s(x). + 0(h²) h2 B.) f"(x) = 2L(x-h)+f(x+3h)+f(x) + 0(h) 2h2 C.) f"(x) = x-h)=3[(x+3h)+2S (x) + Och?) h2 3/(x-h)+f(x+3h)-4ƒ(x) + Och) D.) f"(x) = 6h2 E.) f"(x) = S(x+3h)-f(x-h)+2/(x) + 0(h) 3h2 |arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage