Question

Tangent drawn to $y=a{x}^2+bx+c$ at$(5,4)$ is parallel to $x-axis.$ If $a$ $ϵ$ $[2,4]$. Then maximum value of c.

• A. $54$
• B. $56$
• C. $104$
• D. $106$

Answer 1

Answer: (C)

$104$

$y=a{x}^2+bx+c⟹\frac{dy}{dx}=2ax+b$

At $x=5,y=4⟹25a+5b+c=4$ and also tangent is parallel to $x-axis$

$⟹10a+b=0⟹b=-10a⟹c=4-5b-25a=4+25a$

$a\in [2,4]⟹c\in [54,104]$