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Find f′′(a)=limh→0 (f(a+h)−2f(a)+f(a−h)/h²).

a) f′′ (a)/2
b) f′′ (a)/h²
c) f′′ (a)/3
d) f′′ (a)/6h

1 Answer

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Final answer:

To find the second derivative of a function f(a), we can use the definition of the derivative and the limit definition of the derivative. In this case, the answer is option c) f′′(a)/3.

Step-by-step explanation:

To find the second derivative of a function f(a), we can use the definition of the derivative and the limit definition of the derivative. In this case, we have f′′(a) = limh→0 (f(a+h)−2f(a)+f(a−h)/h²).

To evaluate this limit, we can substitute the given function into the expression and simplify. After simplification, we can take the limit as h approaches 0 to find the second derivative of the function at point a.

Therefore, the answer is the option c) f′′(a)/3.

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