How do I find the numbers #c# that satisfy the Mean Value Theorem for #f(x)=e^(-2x)# on the interval #[0,3]# ?
1 Answer
The Mean Value Theorem guarantees that there exists a number
Let us find such
By Chain Rule,
So, the left-hand side is
Let us find the right-hand side.
by multiplying the numerator and the denominator by
By setting the left-hand side and the right-hand side equal to each other,
By dividing by -2,
By taking the natural log,
By dividing by -2,
by the log property
by simplifying a bit further,