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.

step-by-step explanation:

i could only see the first page. the other pages were blurry. ; -;

x hot dogs for 2$, y drinks for 3$. 29 items and total 70

2x+3y=70

x+y=29

if x=17and y=12

2(17)+3(12)=70

34+36=70

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.