Download App

Increasing and Decreasing Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
Show that $f(x) = (x - 1)e^x + 1$ is an increasing function for all $x > 0$.
✓

Answer

$f(x) = (x - 1)e^x + 1 f'(x) = (x - 1)e^x + e^x= xe^x - e^x + e^x$
$= xe^x$
Given: x > 0
We know,
$e^x> 0$
$\Rightarrow xe^x > 0$
$\Rightarrow f'(x) > 0$, for all $x > 0$
So, f(x) is increasing on for all $x > 0$.

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 "Solve the Following Question.(3 Marks)" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the lengths of the sides of the triangle and also determine the type of a triangle. A(2, -1, 0), B(4, 1, 1,), C(4, -5, 4)
→
Find the inverse of the following matrices $\left[\begin{array}{cc}1 & 2 \\ 2 & -1\end{array}\right]$
→
Find the joint equation of the pair of lines through the origin each of which is making an angle of $30^{\circ}$ with the line
$3 x+2 y-11=0$
→
Evaluate the following integrals:
$\int\frac{2\text{x}^4+7\text{x}^3+6\text{x}^2}{\text{x}^2+2\text{x}}\text{dx}$
→
In $\triangle ABC$, prove that $\sin \left(\frac{ B - C }{2}\right)=\left(\frac{b-c}{a}\right) \cos \left(\frac{ A }{2}\right)$
→
Let $f(x) = x^2 + x + 1$ and $g(x) = sinx$. Show that fog ≠ gof.
→
Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable $x$ is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer ?
→
Show that the points $A(2,-1,0) B(-3,0,4), C(-1,-1,4)$ and $D(0,-5,2)$ are non coplanar.
→
Find the principal solutions of the following equations :

$\sin \theta=-\frac{1}{2}$

→
Solve the following differential equations:dr + (2r cot θ + sin 2θ) dθ = 0
→