COMEDK · Maths · 27. Application of Derivatives
The approximate value of \(f(5.001)\), where \(f(x)=x^{3}-7 x^{2}+15\) is
- A \(-34.995\)
- B \(-33.995\)
- C \(-33.335\)
- D \(-35.995\)
Answer & Solution
Correct Answer
(A) \(-34.995\)
Step-by-step Solution
Detailed explanation
The function is given by \(f(x) = x^{3} - 7x^{2} + 15\). Using the linear approximation formula \(f(x + \Delta x) \approx f(x) + f'(x) \Delta x\), we set \(x = 5\) and \(\Delta x = 0.001\). First, calculate…
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