CGPET 2015 Solved Paper

f(x)={

sin‌(‌ πx 2 )	‌	‌ if ‌x<1
1
3−2x	‌	‌ if ‌x≤1

.
∵ LHL and RHL of f(x) is 1, when x → 1
and f(1)=3−2=1
∴ f(x) is continuous at x = 1
Now, graph of function f(x) is

From the above graph of function, we see that f(x) has local maxima at x = 1.