Asked by UCI Student
Solve the difference quotient for the given function
f(x) = x^3, (f(a+h)-f(a))/h
i forgot how to do this problem
f(x) = x^3, (f(a+h)-f(a))/h
i forgot how to do this problem
Answers
Answered by
drwls
Divide [(a+h)^3 - a^3] by h.
Begin by multiplying out the (a+h)^3 term.
(a+h)^3 = a^3 + 3a^2h + 3ah^2 + h^3.
After two more steps,
(f(a+h)-f(a))/h = 3a^2 + 3ah + h^2
As h-> 0, it approaches 3 a^2, the derivative at x=a.
Begin by multiplying out the (a+h)^3 term.
(a+h)^3 = a^3 + 3a^2h + 3ah^2 + h^3.
After two more steps,
(f(a+h)-f(a))/h = 3a^2 + 3ah + h^2
As h-> 0, it approaches 3 a^2, the derivative at x=a.
Answered by
Reiny
You will need
(x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3
so (f(x+h) - f(x) )/h
= (x^3 + 3x^2h + 3xh^2 + h^3 - x^3)/h
= 3x^2 +3xh + h^2
(x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3
so (f(x+h) - f(x) )/h
= (x^3 + 3x^2h + 3xh^2 + h^3 - x^3)/h
= 3x^2 +3xh + h^2
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