Question

If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).

Answer 1

Hello : 
f'(7) = the slope of the tangent line : let  A(7,4)    B(0,3)
the slope is :   (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
 y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4