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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives2 Marks
Question
Prove that the function does not have maxima or minima: f(x) = ex 
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Answer

f(x) = ex 
$\Rightarrow$ f'(x) = ex 
Now, if f'(x) = 0, then ex = 0 
But, the exponential function can never assume 0 for any value of x.
Therefore, there does not exist c $\in$ R such that f'(c) = 0
Hence, function f does not have maxima or minima.

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