I have another test question i got wrong and didnt undertand soo im hoping someone can help me out.

Show that sqrt(1+x) <1+(1/2)x if x>0 or ( formally written in attachment)

Attachment 18197

I used the formula f'(c)= [f(b)-f(a)]/(b-a) and then just ended up with a mess at the end which is probably why i got it wrong. How would i go abouts starting this problem?