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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

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

Grade:Upto college level

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
f'(x)=2a=2
a=1
f(x)=2x+b
integral f(x)=x^2+bx
putting limits
(9+3b)=7
3b=-2
b=-2/3

sher mohammad
b.tech, iit delhi


bharat bajaj IIT Delhi
askIITians Faculty 122 Points
9 years ago
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

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