MHT CET · Maths · Application of Derivatives
The approximate value of \((3 \cdot 978)^{3 / 2}\) is
- A 7.096
- B 8.096
- C 7.934
- D 8.934
Answer & Solution
Correct Answer
(C) 7.934
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}
& \text { Let } \mathrm{f}(x)=x^{\frac{3}{2}} \\
\therefore \quad & \mathrm{f}^{\prime}(x)=\frac{3}{2} x^{\frac{1}{2}}
\end{array}\)
Here, \(\mathrm{a}=4\) and \(\mathrm{h}=-0.022\).
\(\begin{aligned} & \\ & f(a)=f(4)=4^{\frac{3}{2}}=8 \\ & f^{\prime}(a)=f^{\prime}(4)=\frac{3}{2}(4)^{\frac{1}{2}}=3 \\ & \therefore \quad f(a+h) \approx f(a)+h f^{\prime}(a) \\ & \approx 8+(-0.022)(3) \\ & \approx 8-0.066 \\ & \approx 7.934\end{aligned}\)
& \text { Let } \mathrm{f}(x)=x^{\frac{3}{2}} \\
\therefore \quad & \mathrm{f}^{\prime}(x)=\frac{3}{2} x^{\frac{1}{2}}
\end{array}\)
Here, \(\mathrm{a}=4\) and \(\mathrm{h}=-0.022\).
\(\begin{aligned} & \\ & f(a)=f(4)=4^{\frac{3}{2}}=8 \\ & f^{\prime}(a)=f^{\prime}(4)=\frac{3}{2}(4)^{\frac{1}{2}}=3 \\ & \therefore \quad f(a+h) \approx f(a)+h f^{\prime}(a) \\ & \approx 8+(-0.022)(3) \\ & \approx 8-0.066 \\ & \approx 7.934\end{aligned}\)
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