Question

Suppose the graph of f (x) and the graph of its derivative f ′(x) are shown below. Find an equation to the line tangent to y = f (x) at x = 1.

Answer 1

equation of line tangent to f(x)

y=xf'(x)+c where c is an arbitrary constant .........(1)

u r asked to find equationof tangent to f(x) at x=1 & y=1

replacing x & y by 1 & 1 respectively in equation (1)

1=1f'(1)+c
c=f'(1)-1.....(2)

replacing c in equation (1)

y=xf'(x)+f'(1)-1

Answer 2

well actually i made a mistake in the final equation
'
It is
y=xf'(1)+f'(1)-1

Answer 3

So that would be the final answer correct?