Question

f(x)=e^[a(x^2)+bx+1] , find a and b , if f(1)=f(0)=f'(0) .

Answer 1

Well, f(0) = e^1 and f(1) = e^(a+b+1) hence if f(0) = f(1), it must be that a+b = 0.

Now find the other equation for a and b, using f'(x)

Answer 2

Hmmm.. can you show how?

Answer 3

You need to find the derivative of the function

Answer 4

\[f'(x)=(2ax+b)e^{ax^2+bx+1}\]

Answer 5

Right. Now evaluate that expression at zero, f'(0) and set it equal to the earlier expressions.

Answer 6

Thank you !