MHT CET · Maths · Application of Derivatives
The approximate value of the function \(f(x)=x^{3}-3 x+5\) at \(x=1.99\) is
- A 6.91
- B 6.94
- C 7.94
- D 7.91
Answer & Solution
Correct Answer
(A) 6.91
Step-by-step Solution
Detailed explanation
(D)
\(f(x)=x^{3}-3 x+5 \Rightarrow f^{\prime}(x)=3 x^{2}-3\)
Let \(a=2, h=-0.01\)
\(\therefore f(a)=f(2)=2^{3}-3(2)+5=7\)
\(f^{\prime}(a)=f^{\prime}(2)=3(2)^{2}-3=9\)
We know that \(f(a+h) \neq f(a)+h f^{\prime}(a)\)
\(f(1.99) \div 7-(0.01)(9) \div 7-0.09 \neq 6.91\)
\(f(x)=x^{3}-3 x+5 \Rightarrow f^{\prime}(x)=3 x^{2}-3\)
Let \(a=2, h=-0.01\)
\(\therefore f(a)=f(2)=2^{3}-3(2)+5=7\)
\(f^{\prime}(a)=f^{\prime}(2)=3(2)^{2}-3=9\)
We know that \(f(a+h) \neq f(a)+h f^{\prime}(a)\)
\(f(1.99) \div 7-(0.01)(9) \div 7-0.09 \neq 6.91\)
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