Let
f ( x ) = 1 x − 8 \displaystyle {f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}-{8}}}} f ( x ) = x − 8 1 . Calculate the difference quotient
f ( 6 + h ) − f ( 6 ) h \displaystyle {\frac{{{f{{\left({6}+{h}\right)}}}-{f{{\left({6}\right)}}}}}{{{h}}}} h f ( 6 + h ) − f ( 6 ) for
h = . 1 \displaystyle {h}={.1} h = .1 Preview Question 6 Part 1 of 5 h = . 01 \displaystyle {h}={.01} h = .01 Preview Question 6 Part 2 of 5 h = − . 01 \displaystyle {h}=-{.01} h = − .01 Preview Question 6 Part 3 of 5 h = − . 1 \displaystyle {h}=-{.1} h = − .1 Preview Question 6 Part 4 of 5
If someone now told you that the derivative (slope of the tangent line to the graph) of
f ( x ) \displaystyle {f{{\left({x}\right)}}} f ( x ) at
x = 6 \displaystyle {x}={6} x = 6 was
− 1 n 2 \displaystyle -\frac{{1}}{{n}^{{2}}} − n 2 1 for some integer
n \displaystyle {n} n what would you expect
n \displaystyle {n} n to be?
n = \displaystyle {n}= n = Preview Question 6 Part 5 of 5
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Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)