Suppose that the values of a function
Find as many Taylor polynomials for
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- Prob. 6 (a) (10 point) Let f(x) = 2x² – 3. Find ƒ'(−2) using only the limit definition of derivatives. (b) (10 p.) If ƒ(x) = √√x + 6, find the derivative f'(c) at an arbitrary point c using only the limit definition of derivatives.arrow_forwardLet f(x) = (- 3z - 9)“(6z² – 6) 5 9)*(622 – 6) f'(x) =arrow_forwardFind yy as a function of xx if x^2*y′′+13xy′+36y=x^9 y(1)=−2, y′(1)=−1.arrow_forward
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- Approximate f' (2) using the given data f(0) = 2, f(1) = 3, f(2) = 12, and f(5) = 147 and the Newton's divided-differences interpolation polynomial. O 17 O 10 O 15 O -7 O 12arrow_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_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_forwardFind the derivative of f(x) = V9x8 + 9x (72z + 9)-1/2 (92 + 9x) 1/2(72x + 9) O (928 + 9x)-1/2 -(928 +9x) 3/2(72x7 + 9)arrow_forward
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