TS EAMCET · Maths · Application of Derivatives
The condition that \(f(x)=a x^3+b x^2+c x+d\) has no extreme value, is
- A \(b^2>3 a c\)
- B \(b^2=4 a c\)
- C \(b^2=3 a c\)
- D \(b^2 < 3 a c\)
Answer & Solution
Correct Answer
(D) \(b^2 < 3 a c\)
Step-by-step Solution
Detailed explanation
Given curve is \[ f(x)=a x^3+b x^2+c x+d \] On differentiating w.r.t. \(x\), we get \[ f^{\prime}(x)=3 a x^2+2 b x+c \] For extremum, \(f^{\prime}(x)=0\) \[ \therefore \quad 3 a x^2+2 b x+c=0 \] Since, it has no extremum value…
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