if the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is equal to?

Dear Sonny,

the normal makes an angle 135 degree with the x axis.
also f ''(1)=1 .....[since the tan pie/4=1=slope of normal]
also the graph passes through (1,1) so
f(1)=1,and already proved....
f ''(1)=1
both these are possible only if  f(x)= [x^2 + 1] / 2
hence  f '''' (x) = 1 (ANS)

Regards.

the normal makes an angle 135 degree with the x axis.
also f ''''(1)=1 .....[since the tan pie/4=1=slope of normal]
also the graph passes through (1,1) so
f(1)=1,and already proved....
f ''''(1)=1
both these are possible only if  f(x)= [x^2 + 1] / 2
hence  f '''''''' (x) = 1 (ANS)

Regards.