Consider the function f(x) = cosa, -, . Construct the Lagrange interpolation polynomial which interpolates the function f(x) at o, ₁ = 0 and ₂ = .
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- Determine whether each of the following statements is true or false and explain why. The derivative of a function exists whenever the function is continuous.Determine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.Differentiate. Find f'(t) for f(x) O 17 (2x-7)² O (2x-7)2 O 17 (3x - 2)2 (3x - 2) wwwww. 3x-21
- Let f and g be functions of x, where a is an unknown constant. What is a valid expression for (-)' if f = ax and 12x² - 2ax (4x³+1)² 6ax -1 +² a 6x -4ax² + 2ax (4x³ + 1)² 3 4x +1 ·? XDetermine whether f(x)=sinx+cosx is an odd or even numberFind the greatest and the least values of the function y = x³ – 3x +3 on the 2 (a). interval [-, ].
- Determine whether the given set of functions is linearly independent on the interval (-, ). fi(x) = 3, f2(x) = cos²(x), f3(x) = sin? (x)Find f"(x) for the function f(x) (2+sin x)5*Consider the function f (x) = /5x+25 for the domain [-5, 0). - 1 Find f"(x), where f is the inverse of f. -1 in interval notation. Also state the domain of f f' (x) = O for the domain