Applications of Derivatives
No Critical Point Condition
nta_pyq_2024_apr
Grade 12
Question:
Let the set of all values of $p$, for which $f(x)=(p^2-6p+8)(\sin^2 2x-\cos^2 2x)+2(2-p)x+7$ does not have any critical point, be the interval $(a,b)$. Then $16ab$ is equal to _______.
Step-by-Step Solution
Key Concept: $|1/(2(p-4))|>1\Rightarrow|p-4|<1/2\Rightarrow p\in(7/2,9/2)$.
$16ab=16\cdot(7/2)\cdot(9/2)=252$.
Correct Answer: 252