If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f '(5).

f(5) = 2

f'(5) =

Step-by-step explanation:

Tangent line to a function y = f(x) on a point (5, 2) passes through two points (5, 2) and (0, 1)

Let the equation of the line is,

y - y' = m(x - x')

Slope of a line passing through and =

                                                                                   =

                                                                                   =

Therefore, equation of the line passing through (0, 1) and slope = will be,

y - 1 =

y =

Function representing equation will be,

f(x) =

At x = 5,

f(5) =

     = 1 + 1

     = 2

f(5) = 2

f'(x) =

       =

Therefore, f'(5) = will be the answer.

m∠a is 90°

m∠b is 40°