Given f(x) = x^2 if x<1 and ax^2+bx +c if x ≥ 1 find the values of a and b such that f` (1) exists?

Question

find the values of derivatives, anyone who can help me to solve this problem welcome!!

Answer 1

The question presumably means that b≠0.

 

a=1/2 and b = 1 and c=-(1/2) , i.e. f(x) for x ≥ 1 = (1/2)x² + x - (1/2), then f'(x) = x + 1

f(1)=1 and

and lim (as x approaches 1 from above) f'(x) = 2

and lim (as x approaches 1 from below) f'(x) = 2

and f'(1) = 2