If y = f(x) be the equation of the line touching the line y = 2x + 3 at x = 2, then
Answer & explanation
Correct answer: option 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, $7 f'(2)=2 f(2)$.