TS EAMCET · Maths · Application of Derivatives
The function \(f(x)=x^3+a x^2+b x+c, a^2 \leq 3 b\) has
- A one maximum value
- B no extreme value
- C one maximum and one minimum value
- D one maximum and one minimum value
Answer & Solution
Correct Answer
(C) one maximum and one minimum value
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^3+a x^2+b x+c, a^2 \leq 3 b\). On differentiating w.r.t. \(x\), we get \(\begin{aligned} & f^{\prime}(x)=3 x^2+2 a x+b \\ & \text { Put } \quad f^{\prime}(x)=0 \\ & \Rightarrow \quad 3 x^2+2 a x+b=0 \\ & \end{aligned}\)…
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