For , let satisfy for all . Also, the equation has only one distinct real solution.…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For

a,b\in\mathbb{R}\setminus\{0\}

, let

f(x)=ax^2+bx+a

satisfy

f\left(x+\frac{7}{4}\right)=f\left(\frac{7}{4}-x\right)

for all

x\in\mathbb{R}

. Also, the equation

f(x)=7x+a

has only one distinct real solution. The minimum value of

f(x)

\left[0,\frac{3}{2}\right]

is (a)

-\frac{33}{8}

(b)

0

(c)

4

(d)

-2