Applications of Derivatives
Local Maxima/Minima of Polynomial
nta_pyq_2023_jan
Grade None
Question:
Let $x=2$ be a local minima of the function $f(x)=2x^4-18x^2+8x+12$, $x\in(-4,4)$. If M is the local maximum value of the function f in $(-4,4)$, then M =
$12\sqrt{6}-\dfrac{33}{2}$
$12\sqrt{6}-\dfrac{31}{2}$
$18\sqrt{6}-\dfrac{33}{2}$
$18\sqrt{6}-\dfrac{31}{2}$
Step-by-Step Solution
Key Concept: $f'(x)=8x^3-36x+8=4(2x^3-9x+2)$. $f'(x)=0$ gives $x=2$ (local min) and $x=\frac{\sqrt{6}-2}{2}$ (local max in $(-4,4)$).
$M=12\sqrt{6}-\dfrac{33}{2}$.
Correct Answer: 1