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

Options

A. ` f'(2)=3`
B. ` 2f(2)=7f'(2) `
C. `f(2)+f'(2)+f''(2)=2 `
D. none of these

Answer

B

Explanation

Since ` y=2x+3 ` touches the curve ` y= f(x) ` at `x=2 `
` therefore ((dy)/(dx))_(x=2) =("Slope of the line " y=2x+3 )`
` rArr f'(2)=2 `
Also, ` x=2 rArr y=2 xx 2+3=7 `
Clearly, point (2,7) lies on the curve `y=f(x).`
` therefore 7=f(2) `
Hence, ` 7f'(2)=2f(2).`