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How do you find the derivative of the function: #f(x) = x^3 - 3x^2 - 1# evaluated at x=3?

Answer 1

Ezra Adams

#f'(3)=9#

differentiate each term of f(x) using the #color(blue)"power rule"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))#

#rArrf'(x)=3x^2-6x#

#rArrf'(3)=3(3)^2-6(3)=27-18=9#

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Answer 2

Adam Adkins

To find the derivative of the function ( f(x) = x^3 - 3x^2 - 1 ) evaluated at ( x = 3 ), you first differentiate the function with respect to ( x ) using the power rule for differentiation.

So, ( f'(x) = 3x^2 - 6x ).

Then, substitute ( x = 3 ) into the derivative function:

( f'(3) = 3(3)^2 - 6(3) = 3(9) - 18 = 27 - 18 = 9 ).

Therefore, the derivative of ( f(x) ) evaluated at ( x = 3 ) is ( 9 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.