question archive You are given a function f(x) and told that the function g(x)=a^f(x), a>0, has a slope equal to 2lna at x=0
You are given a function f(x) and told that the function g(x)=a^f(x), a>0, has a slope equal to 2lna at x=0
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You are given a function f(x) and told that the function g(x)=a^f(x), a>0, has a slope equal to 2lna at x=0. Which of the following functions could be f(x).
a) f(x)=x^2
b)f(x)=e^x-1
c) f(x)=2x^2+4x
d)f(x)=2cos(x)-2
e) f(x)=2ln(x+1)
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Option (e) is the correct answer.
Derivative of g is g'(x) = a^f(x) lna f'(x). (We have used chain rule of differentiation.) At x=0 it should be g'(0) = 2 lna. Only f(x) = 2ln(x+1) satisfies this condition. So (e) is the correct option.
