Find the derivative of the function f defined by f(x) = mx + c at… - Vidyadip

Question

Find the derivative of the function f defined by f(x) = mx + c at x = 0.

✓

Answer

Given: f(x) = mx + c
Clearly, being a polynomial function, is differentiable everywhere. Therefore the derivative of f at x is given by:
$\text{f}'(\text{x})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{x}+\text{h}-\text{f(x)})}{\text{h}}$
$\Rightarrow\text{f}'(\text{x})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{m}(\text{x}+\text{h})+\text{c}-\text{mx}-\text{c}}{\text{h}}$
$\Rightarrow\text{f}'(\text{x})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{mx}+\text{mh}+\text{c}-\text{mx}-\text{c}}{\text{h}}$
$\Rightarrow\text{f}'(\text{x})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{mh}}{\text{h}}$
$\Rightarrow\text{f}'(\text{x})=\text{m}$
Thus, $\text{f}'(0)=\text{m}$

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 "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Of the students in a college, it is known that $60\%$ reside in hostel and $40\%$ are day scholars (not residing in hostel). Previous year results report that $30\%$ of all students who reside in hostel attain. A grade and $20\%$ of day scholars attain A grade in their annual examination. At the end of year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

Find the area enclosed by the circle $x^2 + y^2 = a^2$

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:
$\text{h}\text{(x)}=\sin \text{x}-\cos \text{x}, 0< \text{x}<\frac{\pi}{2}$

Find fog and gof if:f(x) = x + 1, g(x) = 2x + 3

A fair die is rolled. Consider events E = $\{1,\ 3,\ 5\},\ \text{F}=\{2,\ 3\}\ \text{and}\ \text{G}=\{2,\ 3,\ 4,\ 5\}.\ \text{Find}:$ $\text{P}\Big[(\text{E}\cup\text{F})|\text{G}\Big]\ \text{and}\ \text{P}\Big[(\text{E}\cap\text{F})|\text{G}\Big]$

A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?

Find the principal value of the following:
$\sec^{-1}\Big(2\sin\frac{3\pi}{4}\Big)$

Evaluate:
$\int\frac{\text{2x.tan-1(x}^{2})}{\text{1 + x}^{4}}\text{dx}. $

Write the value of $\lambda$ for which the lines $\frac{\text{x}-3}{-3}=\frac{\text{y}+2}{2\lambda}=\frac{\text{z}+4}{2}$ and $\frac{\text{x}+1}{3\lambda}=\frac{\text{y}-2}{1}=\frac{\text{z}+6}{-5}$ are perpendicular to each other.

Find the absolute maximum value and the absolute minimum value of the following function in the given intervals:
$\text{f}\text{(x)}=4\text{x}-\frac{1}{2}\text{x}^2 ,\ \text{x}\in\Big[-2,\frac{9}{2}\Big]$