Question #ae316

1 Answer
Jim H
Oct 27, 2015

See the explanation below.

Explanation:

#f(x)=x^2 + 3#

(Note that #f(x+h) = (x+h)^2+3 = x^2+2xh+h^2+3#)

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

# = lim_(hrarr0)(((x+h)^2+3)-(x^2+3))/h# #" "# (form #0/0#)

# = lim_(hrarr0)(x^2+2xh+h^2+3-x^2-3)/h# #" "# (form #0/0#)

# = lim_(hrarr0)(2xh+h^2)/h# #" "# (form #0/0#)

# = lim_(hrarr0)(h(2x+h))/h# #" "# (form #0/0#)

# = lim_(hrarr0)(2x+h) = 2x#

So #f'(x) = 2x#

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