2.3 Differentiation Rules Worksheet - Calculus Maximus Page 2
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6Calculus Maximus
WS 2.3: Differentiation Rules
2
7. For
, find
f x
. Remember to simplify early and often!
f x
x
2
x x
1
x .
(a) find the equation of the tangent line, in Taylor form, to the graph of f at
1
x .
(b) find the equation of the normal line, in Taylor form, to the graph of f at
1
(c) Using your equation from part (b), find the x-intercept of the normal line. Show the work that leads
to your answer.
For 8-10, determine the point(s) (if any) at which the graph of the following functions have horizontal
tangent lines. Justify.
2
8.
y
x
sin , 0
x
x
2
9.
y
3
x
2cos ,
x x
0, 2
10.
f x
2
x
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