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If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to?
Ans) 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 by (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
(x^3-9/5x^2+8/5x-4)
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