KCET · Maths · Application of Derivatives
The range in which \(y=-x^{2}+6 x-3\) is increasing is
- A \(x < 3\)
- B \(x>3\)
- C \(7 < x < 8\)
- D \(5 < x < 6\)
Answer & Solution
Correct Answer
(B) \(x>3\)
Step-by-step Solution
Detailed explanation
Given, \(y=-x^{2}+6 x-3\)
\(\Rightarrow \quad \frac{d y}{d x}=-2 x+6=y^{\prime}\)
\(y\) is increasing, if \(y^{\prime}>0\)
\(\Rightarrow \quad-2 x+6>0\)
\(\Rightarrow \quad-2 x>-6\)
\(\Rightarrow \quad 2 x>6\)
\(\Rightarrow \quad x>3\)
\(\Rightarrow \quad \frac{d y}{d x}=-2 x+6=y^{\prime}\)
\(y\) is increasing, if \(y^{\prime}>0\)
\(\Rightarrow \quad-2 x+6>0\)
\(\Rightarrow \quad-2 x>-6\)
\(\Rightarrow \quad 2 x>6\)
\(\Rightarrow \quad x>3\)
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