If
[tex]f(x)= \left\{ \begin{array}{c}cx+d, \mbox{ } x\leq 2\\ x^2-cx, \mbox{ } x>2[/tex]
and f'(x) is defined at x=2, what is the value of c+d?
If
[tex]f(x)= \left\{ \begin{array}{c}cx+d, \mbox{ } x\leq 2\\ x^2-cx, \mbox{ } x>2[/tex]
and f'(x) is defined at x=2, what is the value of c+d?
a function is continuous at x = a if ...
1. f(a) is defined.
2. lim{x->a} f(x) exists.
3. lim{x->a} f(x) = f(a)
use this definition of continuity for the functions f(x) and f'(x) ... you'll find c and d.
I tried that but then I got the equation
[tex]2c+d=4-2c[/tex]
which is where I got stuck.
The derivative should also be equal at x = 2:
[tex]f'(x) = \left\{ \begin{array}{ll} c & x \leq 2 \\ 2x - c & x > 2[/tex]
Since f'(x) is defined, the deriative at x = 2 can't simultaneously hold 2 values so you can solve for c and then plug it back into the original equation to solve for d.
you did it for f(x) ... did you do it for f'(x)?Originally Posted by tjkubo
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