Question
Question: If for a continuous function f, f(0) = f(1) = 0, f ¢(1) = 2 and y (x) = f (e<sup>x</sup>)e<sup>f(x)<...
If for a continuous function f, f(0) = f(1) = 0, f ¢(1) = 2 and y (x) = f (ex)ef(x), then y ¢(0) is equal to
A
1
B
2
C
0
D
None of these
Answer
2
Explanation
Solution
y(x) = f(ex) ef(x)
y ¢ = f(ex) . ef(x). f ¢(x) + ef(x) f ¢(ex) . ex
y ¢(0) = f(1) . ef(0) . f ¢(0) + ef(0) f ¢(1) = 0 + e°. 2 = 2