Q95 / 180 · COMEDK 2017 · Mathematics

Find the approximate value of $(15)^{\frac{1}{4}}$.

  • Correct answer
    A
    $1.9688$
  • B
    $0.9687$
  • C
    $2.0312$
  • D
    $0.1968$

Solution

Let $f(x)=x^{1 / 4}$ $\Rightarrow \quad f^{\prime}(x)=\frac{1}{4 x^{3 / 4}}$ Now, $a+h=15=16-1$, where $\begin{aligned} &\text { We know, } f(a+h)=f(a)+h f^{\prime}(a) \\ &\Rightarrow f(15) \approx f(16)-1 f^{\prime}(16) \\ &\Rightarrow(15)^{1 / 4} \approx(16)^{1 / 4}-\frac{1}{4(16)^{3 / 4}} \approx 2-\frac{1}{32} \\ &\Rightarrow(15)^{1 / 4} \approx 2-0.03125 \approx 1.9688 \end{aligned}$ $a=16, h=-1$

Hence, the correct answer is option: 'A'.

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