​PLEASE ANSWER CORRECTLY
​PLEASE ANSWER CORRECTLY Ifthe function fix) = ax' + bx2 4 llx— 6 satisfies conditions of Rolle's theorem in [1, 3] and f' O, then values of a and b are respectively

Dear student

fx=ax3+bx2+11x-6f'x=3ax2+2bx+11It is given that Rolle's theorem holds for fx defined on 1,3with c=2+13So, f1=f3 and f'c=0 a+b+11-6=27a+9b+33-6 and  3ac2+2bc+11=0a+b+5=27a+9b+27  and 3a2+132+2b2+13+11=026a+8b+22=0 and 3a4+13+43+4b+2b3+11=026a+8b+22=0 and  12a+a+4a3+4b+2b3+11=0  13a+4b+11=0 and 13a+43a+4b+2b3+11=013a+4b+11=0 and 13a+4b+11+43a+2b3=043a+2b3=0a=1 and b=-6
Regards

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