# Secant Line Slope and Tangent Line Slope

• Aug 26th 2009, 06:11 PM
Secant Line Slope and Tangent Line Slope

Point P=(3,1/9) lies on 1/x^2

Find slope of secant line PQ for certain values of X:

X=2.5, mSecant=-.097778 <You may want to check the mSecant Val.
X=2.9, mSecant=-.077950 for the values.
X=2.99, mSecant=-.074446
X=2.999, mSecant=-.074111
X=3.5, mSecant=-.058957
X=3.1, mSecant=-.070528
X=3.01, mSecant=-.073705
X=3.001,mSecant=-.074037

b)Estimate the value of the slope of the tagent line at curve P. (use 2.999 and 3.001)

and

Using the slope from B find equation for tagent line to the curve at (3,1/9)
• Aug 26th 2009, 06:26 PM
pickslides
Quote:

b)Estimate the value of the slope of the tagent line at curve P. (use 2.999 and 3.001)

$f(x) = \frac{1}{x^2} \Rightarrow f'(x) = \frac{-2}{x^3}$

Find f'(2.999) and f'(3.001) and take an average?

Quote:

Using the slope from B find equation for tagent line to the curve at (3,1/9)

Tangent line is $y-y_1 = m_T(x-x_1)$

In your case $y-\frac{1}{9} = m_T(x-3)$

$m_T$ will be the answer to the previous question
• Aug 26th 2009, 06:30 PM
HallsofIvy
Quote:

Point P=(3,1/9) lies on 1/x^2

Find slope of secant line PQ for certain values of X:

X=2.5, mSecant=-.097778 <You may want to check the mSecant Val.
X=2.9, mSecant=-.077950 for the values.
X=2.99, mSecant=-.074446
X=2.999, mSecant=-.074111
X=3.5, mSecant=-.058957
X=3.1, mSecant=-.070528
X=3.01, mSecant=-.073705
X=3.001,mSecant=-.074037

Yes, these all look good.

Quote:

b)Estimate the value of the slope of the tagent line at curve P. (use 2.999 and 3.001)
You have -.074111 and -.074037 for those two values. The best way to use those two numbers is to average them: [tex]\frac{-.074111-.074037}{2}= \frac{.148148}{2}= 0.074074.

Quote:

and

Using the slope from B find equation for tagent line to the curve at (3,1/9)
so y= 0.074074(x- 3)+ 1/9.
• Aug 26th 2009, 06:40 PM