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The point $P(4, 24)$ lies on the curve $y = x^2 + x + 4$. If $Q$ is the point $(x, x^2 + x + 4 )$, find the slope of the secant line $PQ$ for the following values of $x$.

If $x= 4.1$, the slope of $PQ$ is:

and if $x= 4.01$, the slope of $PQ$ is:

and if $x= 3.9$, the slope of $PQ$ is:

and if $x= 3.99$, the slope of $PQ$ is:

Based on the above results, guess the slope of the tangent line to the curve at $P(4, 24)$.

For this problem, should I just plug in the x values given into the y equation? Then the slope would be...??

HELP! Please!

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    Would you happen to remember how to get the slope of a segment joining two points?2011-10-08
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    You have the point $P(4,24)$ on the curve. If $x=4.1$, what is the corresponding $y$ on the curve? Yes, plug in, you get $Q(4.1,?)$. The problem asks you then to find the **slope** of the line $PQ$, so you are not quite through.2011-10-08
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    What happened to [your other](http://math.stackexchange.com/q/70794/6179), quite related, question? You were asked two questions in the comments there, which were meant to guide you towards a solution, but you answered none. You were also given two answers there, but you reacted to none, commented none and accepted none. Well, well, well...2011-10-08

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