CPM Homework Help : PC Problem 9-82

Use your slopes from problem 9-81 to write the equation of the line which is tangent to each of the functions at the point when $x = 2$ . Use point-slope form.

$f ( x ) = 2 x ^ { 2 }$
Answer (a):
From 9-81, $m = 8$ , $f\left(2\right) = \left(2\right)2^2 = 8$
Equation of line: $y − 8 = 8\left(x − 2\right)$

$f ( x ) = 3 ^ { x }$
Answer (b):
From 9-81, $m = 9.888$ , $y − 9 = 9.888\left(x − 2\right)$
Equation of line: $y = 9.888\left(x − 2\right) + 9$

$f ( x ) = \log x$
Answer (c):
From 9-81, $m = 0.217$ , $f\left(2\right) = \log \left(2\right) = 0.301$
Equation of line: $y − 0.301 = 0.217\left(x - 2\right)$
$y = 0.217\left(x − 2\right) + 0.301$

$f ( x ) = \ \cos x ( x \text { in radians } )$
Answer (d):
From 9-81, $m = −0.909$
$f\left(2\right) = \cos\left(2\right) = −0.416$
Equation of line: $y − \left(−0.416\right) = −0.909\left(x − 2\right)$
$y = −0.909\left(x − 2\right) − 0.416$

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