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Grade: Upto college level

                        

Find all real numbers A , B such that the function f (x) = A.2^x + B, satisfies the conditions f ' (1) = 2 and integral of f (x)dx = 7. where upper limit is 3 , lower limit is 0

6 years ago

Answers : (3)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							
Differentiate the function :
f`(x) = 2A
f`(1) = 2A = 2
Hence, A = 1
Integrate the function :
Ax^2 + Bx : 0 to 3 = 7
9A + 3B = 7
9 + 3B = 7
B = -2/3

Thanks
Bharat Bajaj
askiitians faculty
IIT Delhi
6 years ago
Pushkar Aditya
71 Points
							Given f(x)=A.x^2+B, integration of f(x)=7
           differentiate on both sides
           f`(x)=2*x*A, But f`(1)=2
 Therefore f`(1)=1*2*A
                        2=2A
                  Hence,A=1
Integrate the function:f(x)=A.x^2+B with limits 0 to 3
              Therefore[( A.x^3)/3+Bx] 0 to 3=7
                                 [(x^3)/3+Bx] 0 to 3=7
                                 (27/3+B.3)-(0)=7
                                 9+3B=7
                                 3B=-2
                                   B=-2/3
Therefore A=1 and B=-2/3
						
6 years ago
chaitnyakishore
26 Points
							Given f(x)=A.x^2+B, integration of f(x)=7
           differentiate on both sides
           f`(x)=2*x*A, But f`(1)=2
 Therefore f`(1)=1*2*A
                        2=2A
                  Hence,A=1
Integrate the function:f(x)=A.x^2+B with limits 0 to 3
                 Therefore {[(A.x^3)/3]+Bx}0 to 3=7
                                   (27/3)+B*3=7
                                                3B=7-9
                                                   B=-2/3
Therefore A=1 and B=-2/3
						
6 years ago
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