Question: For each of the following functions, determine the function & that occurs in the theorem below. If fis differentiable at c then Ay = f(c

For each of the following functions, determine the function & that

For each of the following functions, determine the function & that occurs in the theorem below. If fis differentiable at c then Ay = f(c + Ax) - f(c) satisfies Ay = (f'(c) + &)Ax where the function & has the property that lim &(Ax) = 0. AX -0 (a) f(x) = x2- x+ 5 OF = AX(2X - 1 + 4x) OF = 2x - 1 OF = AX O s = (4x ) 2 X (b) f(x) = 2x3 - x - 18 O 8 - 6x2 - 1 O = = AX(6X + 2) O = = AX (6x 2 - 1) O = = 6X(AX ) + 2(4x ) 2 (c) (( x) = -6x4 O = = -24x3 O = = AX(-6 - 24X - 36x2) O E = -6(4x) 3 - 24X(4x) 2 - 36x2(4x) O = = AX(- 24x 3 )

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