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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2022 · Mathematics · Application of Derivatives

In which one of the following intervals is the function...

In which one of the following intervals is the function f(x)=x33−7x22+6x+5f(x)=\frac{x^3}{3}-\frac{7 x^2}{2}+6 x+5 decreasing?

Options

  1. A(−∞,1)(-\infty, 1) only
  2. B(1,6)(1,6)
  3. C(6,∞)(6, \infty) only
  4. D(−∞,1)∪(6,∞)(-\infty, 1) \cup(6, \infty)

Correct answer

B. (1,6)(1,6)

Step-by-step solution

f(x)=x33−7x22+6x+5f′(x)=x2−7x+6=0∴x=1,6\begin{aligned} & f(x)=\frac{x^3}{3}-\frac{7 x^2}{2}+6 x+5 \\ & f^{\prime}(x)=x^2-7 x+6=0 \\ & \therefore x=1,6\end{aligned}
∴f(x)\therefore \mathrm{f}(\mathrm{x}) is decreasing in (1,6)(1,6).
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