you need f and f' to be continuous
lim(x→2-) f'(x) = c
lim(x→2+) f'(x) = -4-c
So, you need c = -4-c => c = -2
lim(x→2-) f(x) = 2c+d = -4+d
lim(x→2+) f(x) = -4+4 = 0
so, -4+d = 0 => d=4
S, f(x) =
{-2x+4 for x≤2
{-x^2+2x for x>2
See the graphs at
https://www.wolframalpha.com/input/?i=plot+y%3D-2x%2B4%2C+2x-x%5E2
f (x)={cx+d for x≤2
{-x^2−cx for x>2
Let f be the function defined above, where c and d are constants. If f is differentiable at x=2, what is the value of c+d ?
-4, -2, 0, 2, 4
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