How do you use the definition of a derivative to find the derivative of #f(x)= 2x^2 - 3x+4#?

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Answer 1 · 2016-10-31T23:57:25

# f'(x) = 4x-3#

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

So, with # f(x)=2x^2-3x+4 # we have:
# f'(x) = lim_(hrarr0)( ( (2(x+h)^2-3(x+h)+4) - (2x^2-3x+4) ) / h ) #

# :. f'(x) = lim_(hrarr0)( ( ( 2(x^2+2hx+h^2)-3x-3h+4) - (2x^2-3x+4) ) /h )#

# :. f'(x) = lim_(hrarr0)( ( 2x^2+4hx+2h^2-3x-3h+4 - 2x^2+3x-4) /h )#

# :. f'(x) = lim_(hrarr0)( ( 4hx+2h^2-3h) /h )#

# :. f'(x) = lim_(hrarr0)( 4x+2h-3 )#

# :. f'(x) = 4x-3#