TS EAMCET · Maths · Application of Derivatives
The approximate value of \(y=(1.01)^3+2(1.01)^{\frac{3}{2}}+5\) is
- A 8.06
- B 8.04
- C 8.02
- D 8.16
Answer & Solution
Correct Answer
(A) 8.06
Step-by-step Solution
Detailed explanation
Let the function be \[ y=f(x)=x^3+2 x^{3 / 2}+5 \] Differentiate w.r.t. ' \(x\) ' \[ f^{\prime}(x)=3 x^2+2 \cdot \frac{3}{2} x^{1 / 2}=3 x^2+3 x^{1 / 2} \] Let \(x=1\) and \(\Delta x=0.01\) So, \[ f(1)=1^3+2(1)^{3 / 2}+5=1+2+5=8 \] Now,…
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