Home > Calculus > Slope of a Curve at a Point

How do you find the slope of the secant lines of #f(x) = 2/x + 2# through the points: (0, f(0)) and (0+h, f(0+h))?

Answer 1

Samantha Adkison

This is not possible, because #f(0)# does not exist.

So there is no point #(0,f(0))#.

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Answer 2

Luke Alvarez

To find the slope of the secant line between two points on a function (f(x)), you use the formula:

[ \text{Slope} = \frac{f(0+h) - f(0)}{(0+h) - 0} ]

So, for the given function (f(x) = \frac{2}{x} + 2), the slope of the secant line through the points ((0, f(0))) and ((0+h, f(0+h))) is:

[ \text{Slope} = \frac{f(0+h) - f(0)}{(0+h) - 0} = \frac{\frac{2}{0+h} + 2 - (2)}{h} ]

[ = \frac{\frac{2}{h} + 2 - 2}{h} = \frac{\frac{2}{h}}{h} = \frac{2}{h^2} ]

Therefore, the slope of the secant line is (\frac{2}{h^2}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.