KCET · Maths · Continuity and Differentiability
The function \( f(x)=x^{2}+2 x-5 \) is strictly increasing in the interval
- A \( (-1, \infty) \)
- B \((-\infty,-1) \)
- C \( [-1, \infty) \)
- D \( (-\infty,-1) \)
Answer & Solution
Correct Answer
(C) \( [-1, \infty) \)
Step-by-step Solution
Detailed explanation
Given function, \(f(x)=x^{2}+2 x-5\)
We know that, for strictly increasing function \(f^{\prime}(x)>0\)
So, \(2 x+2>0\)
\(\Rightarrow x>-1\)
Therefore, function \(f(x)=x^{2}+2 x-5\) is strictly increasing in the interval \(x \in[-1, \infty)\)
We know that, for strictly increasing function \(f^{\prime}(x)>0\)
So, \(2 x+2>0\)
\(\Rightarrow x>-1\)
Therefore, function \(f(x)=x^{2}+2 x-5\) is strictly increasing in the interval \(x \in[-1, \infty)\)
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