Question
Question: If f(x) = p \| sin x\| + qe<sup>\|x\|</sup> + r\|x\|<sup>3</sup> and if f(x) is differentiable at x ...
If f(x) = p | sin x| + qe|x| + r|x|3 and if f(x) is differentiable at x = 0, then
A
p = q = r = 0
B
p + q = 0; r is any real number
C
q + r = 0; p is any real number
D
r = 0; p = 0, q is any real number
Answer
p + q = 0; r is any real number
Explanation
Solution
It can be seen f¢(0–) = –p –q and f¢(0+) = p + q. Therefore, for f to be differentiable at x = 0, we must have p + q = 0.