Question:
If \( f \) is differentiable and \( \lim_{h\to0} \frac{f(1+h)-f(1)}{h}=5 \), find \( f'(1) \)
If \( f \) is differentiable and \( \lim_{h\to0} \frac{f(1+h)-f(1)}{h}=5 \), find \( f'(1) \)
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Recognize derivative definition instantly in limits.
Updated On: May 1, 2026
- \( 0 \)
- \( 1 \)
- \( 3 \)
- \( 4 \)
- \( 5 \)
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The Correct Option is
Solution and Explanation
Concept: Definition of derivative.
Step 1: Recall: \[ f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h} \]
Step 2: Compare given expression.
Step 3: Here \( a=1 \).
Step 4: So directly: \[ f'(1)=5 \]
Step 5: Final answer confirmed.
Step 1: Recall: \[ f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h} \]
Step 2: Compare given expression.
Step 3: Here \( a=1 \).
Step 4: So directly: \[ f'(1)=5 \]
Step 5: Final answer confirmed.
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