JEE PYQ: Application Of Derivatives Question 18
Question 18 - 2021 (25 Feb Shift 1)
Let $f(x)$ be a polynomial of degree 6 in $x$, in which the coefficient of $x^6$ is unity and it has extrema at $x = -1$ and $x = 1$. If $\lim_{x \to 0} \frac{f(x)}{x^3} = 1$, then $5 \cdot f(2)$ is equal to
Show Answer
Answer: 144
Solution
$f(x) = x^6 + ax^5 + bx^4 + x^3$. Since $f’(1) = 0$ and $f’(-1) = 0$: $6 + 5a + 4b + 3 = 0$ and $-6 + 5a - 4b + 3 = 0$. Solving: $a = -\frac{3}{5}$, $b = -\frac{3}{2}$. $5 \cdot f(2) = 5[64 - \frac{96}{5} - 24 + 8] = 144$.
BETA
