When is the function f(x) = e^{ax} monotonica | vedclass

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Question

(C) Let the function be $f(x) = e^{ax}$.To find the intervals where the function is monotonically decreasing,we calculate the first derivative:$f'(x)

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When $a < 0$

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(C) Let the function be $f(x) = e^{ax}$.To find the intervals where the function is monotonically decreasing,we calculate the first derivative:$f'(x) = \frac{d}{dx}(e^{ax}) = a \cdot e^{ax}$.$A$ function is monotonically decreasing if $f'(x) Since the exponential function $e^{ax}$ is always positive for all real $x$ $(e^{ax} > 0)$,the sign of $f'(x)$ depends entirely on the constant $a$.Therefore,$f'(x) Thus,the function $f(x) = e^{ax}$ is monotonically decreasing when $a < 0$.

When is the function $f(x) = e^{ax}$ monotonically decreasing?

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