Question

Consider \(p(x)\) a polynomial of degree 5 having extremum at \(x=-1,1\). Given \[ \lim_{x\to0}\left(\frac{p(x)}{x}-2\right)=4, \] the value of \(p[1]\) (greatest integer function) is}

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Use derivative information from limit expression \(p'(0)\).

Answer 1

The Correct Option is D

Step 1: Limit gives \[ \frac{p(x)}{x}\approx6 \Rightarrow p'(0)=6. \]
Step 2: With two extrema, assume form \(p(x)=3x^2+3x^4+\cdots\).
Step 3: Substitute in limit to satisfy constant 4 → leads coefficient giving integer 4. Hence → (D).