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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 bharat bajaj
IIT Delhi
122 Points
```							Differentiate the function :f`(x) = 2Af`(1) = 2A = 2Hence, A = 1Integrate the function :Ax^2 + Bx : 0 to 3 = 79A + 3B = 79 + 3B = 7B = -2/3ThanksBharat Bajajaskiitians facultyIIT Delhi
```
6 years ago
```							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
```							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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