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(Solved): Consider the function \( f(x)=4 e^{\frac{x}{5}} \) on the interval [n. \( \left..5\right] \).
Find ...
Consider the function \( f(x)=4 e^{\frac{x}{5}} \) on the interval [n. \( \left..5\right] \).
Find the average or mean slope of the function on this interval. Enter at least 4 decimal places in your answer. By the Mean Value Theorem, we know there exists a \( c \) in the open interval \( (0,5) \) such that \( f^{\prime}(c) \) is equal to this mean slope. For this problem, there is only one \( c \) that works. Find it. Enter at least 4 decimal places in your answer.