How do you find f'(2) using the limit definition given #f(x)= 9-x^2#?

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Answer 1 · 2017-01-09T16:47:28

-4

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Answer 2 · 2017-01-09T16:50:31

-4

Using the limit definition, you get:

#f'(2)=lim_(x->2)(f(x)-f(2))/(x-2)#

#=lim_(x->2)((9-x^2)-(9-2^2))/(x-2)#

#=lim_(x->2)(9-x^2-5)/(x-2)#

#=lim_(x->2)(4-x^2)/(x-2)#

#=lim_(x->2)-(x^2-4)/(x-2)#

#=lim_(x->2)-(cancel((x-2))(x+2))/cancel(x-2)#

#=-(2+2)=-4#