Question:
If \( f(x) = 3x^2 - 7x + 5 \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \) is equal to
If \( f(x) = 3x^2 - 7x + 5 \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \) is equal to
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This limit directly represents derivative at a point — recognize it instantly.
Updated On: May 8, 2026
- 6
- \(-7\)
- 7
- \(-6\)
- 5
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The Correct Option is B
Solution and Explanation
Concept:
\[
\lim_{x\to 0} \frac{f(x)-f(0)}{x} = f'(0)
\]
Step 1: Differentiate function
\[ f'(x) = 6x - 7 \]
Step 2: Evaluate at \(x=0\)
\[ f'(0) = -7 \]
Step 3: Alternative verification
\[ f(0)=5 \] \[ f(x)-f(0)=3x^2-7x \] \[ \frac{f(x)-f(0)}{x} = 3x - 7 \]
Step 4: Take limit
\[ x \to 0 \Rightarrow -7 \]
Step 5: Final Answer
\[ \boxed{-7} \]
Step 1: Differentiate function
\[ f'(x) = 6x - 7 \]
Step 2: Evaluate at \(x=0\)
\[ f'(0) = -7 \]
Step 3: Alternative verification
\[ f(0)=5 \] \[ f(x)-f(0)=3x^2-7x \] \[ \frac{f(x)-f(0)}{x} = 3x - 7 \]
Step 4: Take limit
\[ x \to 0 \Rightarrow -7 \]
Step 5: Final Answer
\[ \boxed{-7} \]
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