If y = f(x) be the equation of the line touching the line y = 2x + 3 at x = 2, then

$f'(2)=3$ $2 f(2)=7 f'(2)$ $f(2)+f'(2)+f''(2)=2$ none of these

$2 f(2)=7 f'(2)$

Since $y=2 x+3$ touches the curve y = f(x) at x = 2. ∴  $\left(\frac{d y}{d x}\right)_{x=2}$ = (Slope of the line y = 2x + 3) ⇒  f'(2) = 2 Also, $x=2 \Rightarrow y=2 \times 2+3=7$ Clearly, point (2, 7) lies on the curve y = f(x). ∴  7 = f(2) Hence, $7 f'(2)=2 f(2)$.