Evaluate the difference quotient for the given function. Simplify your answer. f(x)=X^3, f(a+h)-frac{a}{h}

bobbie71G 2020-12-25 Answered
Evaluate the difference quotient for the given function. Simplify your answer. f(x)=X3,f(a+h)ah
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Expert Answer

Tuthornt
Answered 2020-12-26 Author has 107 answers
f(a+h)f(a)h
It is given that f(x)=x3
=(a+h)3a3h
Recall that: A3B3=(AB)(A2+AB+B2)
=(a+ha)(a+h)2+a(a+h)+a2h
=(h)[(a2+2ah+h2)+(a2+ah)+a2]h
Cancel h from both the numerator and the denominator
=3a2+3ah+h2
Result
3a2+3ah+h2
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