AP EAMCET · Maths · Application of Derivatives
\(y=x^3-a x^2+48 x+7\) is an increasing function for all real values of \(x\), then \(a\) lies in the interval
- A \((-14,14)\)
- B \((-12,12)\)
- C \((-16,16)\)
- D \((-21,-21)\)
Answer & Solution
Correct Answer
(B) \((-12,12)\)
Step-by-step Solution
Detailed explanation
Given, equation \(y=x^3-a x^2+48 x+7\) Differentiating the above equation with respect to the variable \(x\), we have \(\frac{d y}{d x}=3 x^2-2 a x+48\) Thus, above function is a quadratic function. So, \(D < 0\). In \(y^{\prime}=3 x^2-2 a x+48, A=3, B=-2 a\) and \(c=48\)…
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