Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
Question
Show that the function given by f(x) = 3x + 17 is increasing on R.
✓

Answer

Let $x_1$ and $x_2$ be any two numbers in R such that
$x_1$ < $x_2$
$\Rightarrow$ $3x_1 < 3x_2$
$\Rightarrow$ $3x_1 + 17 < 3x_2 + 17$
$\Rightarrow$ $f(x_1) < f(x_2)$
Therefore, f is strictly 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 "1 Marks Question" from Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Integrate the function $x^2 \log x$
→
State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
X 0 1 2 3 4
P(X) 0.1 0.5 0.2 -1 0.3
→
Evaluate the following:
$\cot^{-1}\Big(\cot\frac{9\pi}{4}\Big)$
→
Find that interval in which the function $f(x)=x^2-1$ is increasing.
→
Write the order of the differrntial quation associated with the primitive $\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\text{e}^{-2\text{x}+\text{C}_{4}}$ where $C_1, C_2, C_3, C_4$ are arbitrary constants.
→
Integrate the functions in Exercises:
$\frac{\text{x}^3\sin\big(\tan^{-1}\text{x}^4\big)}{1+\text{x}^8}$
→
$\int \sqrt{1+x^{2}} d x$ is equals to
→
Evaluate: $\int\text{(1-x)}\sqrt{x}\text{dx}.$
→
Integrate the functions in Exercises:
$\text{x}\sqrt{1+2\text{x}^2}$
→
Write the value of the determinant $\begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6\text{x} & \text{9x} & 12\text{x} \end{vmatrix} $
→