if f(1)=10 and f'(x)>=2 for all x in the domain 1<=x<=4, what is the smallest possible value of f(4)?

lets look at the mininmum f', which is 2.

the f(x)=m*x + b
f(1)=10=2*1+B or b is 8
so minumum f(4)=2*4+8=16