Limits, Continuity & Differentiability
Differentiation
nta_abhyas_2025
Grade 12
Question:
If $f(x) = \begin{cases} x+1; & x > 1 \\ 0; & x = 1 \text{ then } f'(0) \text{ equals to} \\ -3x; & x < 1 \end{cases}$
Step-by-Step Solution
Key Concept: Direct computation of the derivative of a linear function
Given that $f(x) = 7 - 3x$ for $x < 1$, we find $f'(x) = -3$. At $x = 0$, we have $f'(0) = -3$.
Correct Answer: 3