Download App

Differentiation and it's Applications — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsDifferentiation and it's Applications2 Marks
Question
Show that the function $f(x)=x^3-3 x^2+6 x-100$ is increasing on R.
✓

Answer

$f(x)=x^3-3 x^2+6 x-100$
$f^{\prime}(x)=3 x^2-6 x+6$
$=3\left[x^2-2 x+2\right]=3\left[(x-1)^2+1\right]$
since $f^{\prime}(x)>0 ; x \in R$
$\therefore f(x)$ is increasing on $R$.

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 Differentiation and it's Applications→Differentiation and it's Applications — all question types→Applied Maths STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Prove that: 3500 ≡ 2 (mod 7)
→
In a 1000 metres race. A, B, and C get the gold, silver, and bronze medals, respectively. If A beats
B by 100 metres and B beats C by 100 metres, then by how many metres does A beat C?
→
In a 100 m race, A runs at 8 km/h. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
→
If $A$ is square matrix of order 3 such that $|\operatorname{adj} A|=64$, then find $|A|$.
→
From the differential equation of equation y = a cos 2x + b sin 2x where a and b are constants.
→
The total cost function (in thousands) for manufacturing x manipulators per year is given $C(x)=375+25 x-0.25 x^2 \quad 0 \leq x \leq 50$
(a) Use the marginal cost function to approximate the cost of producing the $31^{s t}$ manipulator.
(b) Use the total cost function to find the exact cost of producing the $31^{s t}$ manipulator.
→
A man can row upstream at 7 km/h and downstream at 10 km/h. Find man's rate in still water and rate of current.
→
If $3 A-B=\left[\begin{array}{ll}5 & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}4 & 3 \\ 2 & 5\end{array}\right]$, then find the matrix $A.$
→
A cistern can be filled by pipes A and B in 4 hours and 6 hours respectively. When full, the cistern can be emptied by pipe C in 8 hours. If all the pipes were turned on at the same time, in how much time will the cistern be filled?
→
How much water must be added to 60 litres of milk at $1 \frac{1}{2}$litres for ₹ 20 so as to have a mixture worth ₹ $10 \frac{2}{3}$a litre ?
→