How do you use the limit definition to find the slope of the tangent line to the graph # f(x) = x^2#?

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How do you use the limit definition to find the slope of the tangent line to the graph # f(x) = x^2#?

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Answer 1 · 2016-10-21T15:34:34

# f'(x) = 2x #

Explanation:

By definition # f'(x) = d/dxf(x) = lim_{h->0) (f(x+h)-f(x))/h #

So if # f(x)=x^2# then:

# f'(x) = lim_{h->0) ((x+h)^2-x^2)/h #
# :. f'(x) = lim_{h->0) (x^2+2hx+h^2-x^2)/h #
# :. f'(x) = lim_{h->0) ( 2hx+h^2 )/h #
# :. f'(x) = lim_{h->0) ( 2x+h ) #
# :. f'(x) = 2x #

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How do you use the limit definition to find the slope of the tangent line to the graph # f(x) = x^2#?

1 Answer

Explanation:

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