AP EAMCET · Maths · Application of Derivatives
The curve \(y=a x^3+b x^2+c x+5\) touches \(X\)-axis at \(P(-2,0)\), then \(c=\)
- A \(4 a+5\)
- B \(4 a-5\)
- C \(5-4 a\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(4 a+5\)
Step-by-step Solution
Detailed explanation
\(y=a x^3+b x^2+c x+5\) ...(i) \(\because\) It passes through \((-2,0)\) \(\therefore \quad 0=-8 a+4 b-2 c+5\) ...(ii) \(\begin{aligned} & \Rightarrow \frac{d y}{d x}=3 a x^2+2 b x+c \\ & \Rightarrow\left[\frac{d y}{d x}\right]_{(-2,0)}=12 a-4 b+c\end{aligned}\) According to…
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