COMEDK · Maths · 27. Application of Derivatives
The approximate value of \(f(5.001)\), where \(f(x)=x^3-7 x^2+10\)
- A -39.995
- B -38.995
- C -37.335
- D -40.995
Answer & Solution
Correct Answer
(A) -39.995
Step-by-step Solution
Detailed explanation
First, break the number 5.001 as \(x=5\) and \(\Delta x=0.001\) and use the relation \(\begin{aligned} & f(x+\Delta x) \approx f(x)+\Delta x f^{\prime}(x) \\ & \text { consider } f(x)=x^3-7 x^2+10 \Rightarrow f^{\prime}(x)=3 x^2-14 x \end{aligned}\) Therefore,…
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