let f(x)=x2-1,x≤1
nd f(x)=k(x-1),x>1
then
a)f is continuous for only finitely many values of k
b)f is discontinuous at x=1
c)f is differentiable only when k=2
d)there r infinitely many values of k for which f is differentiable
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1 Answers
62dear this one is simple.. sort of...
The limit of both when approaching 1 is 0..
i mean LH for the 1st term and RH limit for 2nd term..
so a and b are eliminated.
now derivative on the LH derivative is 2x (prove!)
RH derivative is k
for this function to be differentiable
LH Derivative = RH derivative
so k=2!