How do you use the definition of a derivative to find the derivative of $f(x) = 5x + 9$ at x=2?

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How do you use the definition of a derivative to find the derivative of $f(x) = 5x + 9$ at x=2?

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Answer 1 · 2016-10-31T23:15:57

$f'(2) = 5$

Explanation:

By definition $f'(x) =lim_(hrarr0)( (f(x+h)-f(x))/h )$

So, with $f(x) = 5x+9$ we have:

$f'(2) = lim_(hrarr0)( ( f(2+h) - f(2) ) / h )$
$:. f'(2) = lim_(hrarr0)( ( (5(2+h)+9) - (5(2)+9) ) / h )$
$:. f'(2) = lim_(hrarr0)( ( (10+5h+9) - (10+9) ) / h )$
$:. f'(2) = lim_(hrarr0)( ( 10+5h+9 - 10-9 ) / h )$
$:. f'(2) = lim_(hrarr0)( (5h) / h )$
$:. f'(2) = lim_(hrarr0)( 5 )$
$:. f'(2) = 5$

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How do you use the definition of a derivative to find the derivative of $f(x) = 5x + 9$ at x=2?

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Explanation:

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How do you use the definition of a derivative to find the derivative of f(x) = 5x + 9 f(x) = 5x + 9 at x=2?

1 Answer

Explanation:

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How do you use the definition of a derivative to find the derivative of $f(x) = 5x + 9$ at x=2?