Let f(x) be a polynomial of degree 4 and f2=−1,f'2=0,f''2=2,f'''2=−12,f''''2=24 then find f''1=

Letfx=ax4+bx3+cx2+dx+e⇒f2=−1⇒16a+8b+4c+2d+e=−1→1f'x=4ax3+3bx2+2cx+d⇒f'2=0⇒32a+12b+4c+d=0→2f"x=12ax2+6bx+2c⇒f"2=2⇒48a+12b+2c=2→3f"'x=24ax+6b⇒f'''2=−12⇒48a+6b=−12→4f""x=24a⇒f""2=24⇒24a=24⇒a=14⇒48+6b=−12⇒6b=−60⇒b=−103⇒48−120+2c=2⇒2c=74⇒c=372⇒32−120+148+d=0⇒d=−60f''1=12112+6−101+237=12−60+74=26