Suppose that the values of a function
Find as many Taylor polynomials for
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CALCULUS EARLY TRANSCENDENTALS W/ WILE
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- Let f(x) = (- 3z - 9)“(6z² – 6) 5 9)*(622 – 6) f'(x) =arrow_forwardWrite all answers with numbers rounded to two decimal places. In Calculus the derivative of mononomial function is given in the following way. If the function is f (x) = a x" then the derivative is f'(x) = an x(-1). If the function is f(x) = 7x then the derivative is f'(x) an*x^(n-4) If the function is f(x) 5x 2 then the derivative is f'(x) = an*2^(n-1) If the function isf (x) = 3.8x then the derivative is f'(x) = an*x^(n-2) Your last answer was interpreted as follows: an · x"-4 The variables found in your answer were: an, n, x Your last answer was interpreted as follows: an · 2.2n-1arrow_forwardCompute the derivative of the following using product or quotient rules. nedino nt 1. g(x) = x(2x5 – 6x3 + 10) X+ 1 2. y = ---- X- 1 -- 3. y = (x3 – 5x)(3x2 + x) d 4. --- (Vx- x + 1)(2x + Vx ) dxarrow_forward
- 1. Assume that the function is a one-to-one function. (a) If f(2) = 5, find f-'(5). Your answer is (b) If ƒ -'(– 8) : 5, find f( – 5). Your answer is 2. If f is one-to-one and f(13) = 9, then f-'(9) : - 1 and (f(13)) 3. Use the table below to fill in the missing values. f(x) 1 3 2 8 7 4 2 6 4 7 9. 6 9 f(7) = if f(x) = 2 then z = f(9) = if f-(x) = 5 then a = 4. (a) Find the inverse function of f(x) = 9x – 7. f-'(x) (b) The graphs of f and f 1 are symmetric with respect to the line defined by y =arrow_forwardLet f be a function that has derivatives of all orders on the interval (5, 7). Use the values in the table below and the formula for Taylor polynomials to give the 4" degree Taylor polynomial for f centered at x = = 6: f(6) f'(6) f"(6) | f"(6) | f(4)(6) -3 4 8 9. -3 3 x³ + 4x² + 4x – 3 1 b) O-3 + 4 (x + 6) +4(x + 6)° + 2(x + 6)3. 8 3 c) O-3 + 4 (x – 6) + 4(x – 6)² + x – 6)³ - (x – 6)* d) O-3x* + 9x³ + 8x2 + 4x – 3 e) O-3 +4 (x – 6) + 8(x – 6)² + 9(x – 6)³ – 3(x – 6)* f) O-3 + 4 (x + 6) + 8(x + 6)² + 9(x + 6) – 3(x + 6)* g) None of the above.arrow_forwardFind (f-1)'(9) if f(x)=x3+x-1arrow_forward
- 3. Let f (x) = (3x2 + 1)?. Find f'(x)in 3 different ways by following the instructions below in parts a, b and c: a) Algebraically multiply out the expression for f (x) and expand, then take the derivative. b) View f (x) as (3x? +1)(3x2 + 1) and use the product rule to find f' (x). C) Apply the chain rule directly to the expression f (x) = (3x² + 1)?. d) Are your answers in parts a, b, c the same? Why or why not?arrow_forwardFind f'(x) and simplify. X X - 19 f(x) = Which of the following shows the correct application of the quotient rule? O A. O B. O C. O D. f'(x) = (x)(1)-(x-19) (1) [x - 191² (x-19)(1)-(x)(1) [x-19]² (x)(1)(x-19) (1) [x]² (x-19)(1)-(x)(1) [x]²arrow_forwardLet f(x) be a one-to-one function such that f(2)=5 and f'(2)=-4. Find f(-1)'(5)arrow_forward
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