TS EAMCET · Maths · Application of Derivatives
Observe the following statements A : \(f(x)=2 x^3-9 x^2+12 x-3\) is increasing outside the interval \((1,2)\) \(\mathrm{R}: f^{\prime}(x) < 0\) for \(x \in(1,2)\). Then, which of the following is true?
- A Both A and R are true, and R is not the correct reason for A
- B Both A and R are true, and R is the correct reason for A
- C A is true but R is false
- D A is false but R is true
Answer & Solution
Correct Answer
(A) Both A and R are true, and R is not the correct reason for A
Step-by-step Solution
Detailed explanation
Statement A \(f(x)=2 x^3-9 x^2+12 x-3\) ...(i) \(f^{\prime}(x)=6 x^2-18 x+12\) ...(ii) For increasing function, \(f^{\prime}(x)>0\)…
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