Calculus T/F
Level
2
True or False. To find the linear approximation to a function at x = a you need to know the first derivative of that function.
False
True
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1 solution
True. The linear approximation L(x) to a function f(x) is given by
L ( x ) = f ( a ) + ( x − a ) f ′ ( a )
Where f' is the derivative of f. Since the definition of the linear approximation includes the definition of the derivative pertaining to that function, the derivative is required to solve for linear approximation.