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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 9 Differentiability Exercise 9.2 Question 6 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 9 Differentiability Exercise 9.2 Question 6 Maths Textbook Solution.

Answers (1)

Answer: f'\left ( 0 \right )=m

Hint:  Differentiate f(x) to find f `(x). Put x = 0 in f `(x).

Given:f\left ( x \right )=mx+c

Solution:

Differentiating f(x) w.r.t x then,

\Rightarrow \frac{d}{dx}\left \{ f\left ( x \right ) \right \}=\frac{d}{dx}\left ( mx+c \right )

                           =\frac{d}{dx}\left ( mx \right )+\frac{d}{dx}\left ( c \right )

                            \begin{aligned} &{\left[\because \frac{d}{d x}(a x+b)=\frac{d}{d x}(a x)+\frac{d}{d x}(b)\right]} \\ &=m \frac{d}{d x}(\mathrm{x})+\frac{d}{d x}(\mathrm{c}) \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[\because \frac{d}{d x}\left(a x^{n}\right)=a \frac{d}{d x}\left(x^{n}\right)\right] \end{aligned}

                            m=\left ( 1x^{1-1} \right )+0                                \left[\because \frac{d}{d x} \text { (constant) }=0,\left[\because \frac{d}{d x}\left(x^{n}\right)=n x^{n-1}\right]\right]

\therefore f `(x) = m

For f `(0), put x = 0 in f `(x), then

f `(x) = m

\Rightarrow f ` (x) is not affected at x = 0, since in f `(x) there is no term of x.

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