Prove that the function does not have maxima or minima: f(x) = e^… - Vidyadip

Question

Prove that the function does not have maxima or minima: $f(x) = e^x$

✓

Answer

$f(x) = e^x$
$\Rightarrow f'(x) = e^{x }$
Now, if $f'(x) = 0,$ then $e^x = 0$
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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Application of Derivatives→Application of Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate: $\int \frac{x^2 \tan ^{-1} x}{\left(1+x^2\right)} d x$

Write the value of $\lambda$ so that vectora $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ are perpendicular to each other.

If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$\vec{\text{a}}+2\vec{\text{b}}+3\vec{\text{c}},\ 2\vec{\text{a}}+\vec{\text{b}}+3\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are mutually perpendicular unit vectors, write the value of $\big|\vec{\text{a}}+\vec{\text{b}}\big|.$

Write the distance of the plane $\vec{\text{r}}.(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})=12$ form the origin.

Find an angle $\theta,0<\theta<\frac{\pi}{2},$ which increases twice as fast as its sine.

Find the principal value of the following:
$\sec^{-1}(2)$

If $\vec { a } \cdot \vec { a } = 0$ and $\vec { a } \cdot \vec { b } = 0,$ then what can be concluded about the vector $\vec { b }$?

Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that
none is a spade?

A is a skew-symmetric of order 3, write the value of |A|.