<p>If y= f(x) = x/(1+x), consider the points (1, .5) and (3, .75) which lie on the graph of this function.</p>
<p>A. Calculate the slope of the secant line when x=1.01
B. If the slope of the tangent line to the curve at x=1 is .25, what is the equation of this tangent line?</p>
<p>Hey. I'm guessing you aren't into derivatives yet. Here's some help:</p>
<p>A) The slope of the secant line is obtained using the slope formula. First, find the y-coordinate that goes along with the x-coordinate 1.01. This is 1.01/2.01, or about .5025. You use the points (1, .5) and (1.01, .5025) in the slope formula to get the slope of the secant : (.5025-.5)/(1.01-1)= .25</p>
<p>B) If the slope is .25, you can use the formula y=mx+b to find the tangent line. m is the slope, .25. You can't find out b until you plug a point into the equation. Since the line is tangent to the point (1, .5), it must include that point. So .5=(.25)(1)+b ----> .5=.25+b -------> b=.25
Thus the tangent line is y=.25x+.25. </p>
<p>Hope that helped.</p>
<p>Weird, I had that exact problem last night. I think chris07 covered it, good luck in Calc!</p>