Question

Estimate - tangent line:

http://i.imgur.com/u4xnZ2O.png

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I would like to know what is the procedure to solve this problem.

Answer 1

tangent line approximation

Answer 2

find the equation of tangent line

Answer 3

Notice that the tangent is passing thru two points :
(5, 3) and (9, 6)

Answer 4

can u write the equation ?

Answer 5

is this the formula i need to use y-f(a)=f'(a)(x-a)?

Answer 6

yes f'(a) = slope of tangent

Answer 7

equation for tangent thru two points :
(5, 3) and (9, 6)


y - 3 = 3/4(x-5)

Answer 8

y = 3 + 3/4(x-5)

Answer 9

around x = 5,

\(f(x) \approx 3 + \frac{3}{4}(x-5) \)

Answer 10

to estimate f(4.9), plugin x = 4.9 in above tangent equation

Answer 11

\(f(4.9) \approx 3 + \frac{3}{4}(4.9-5) \)

Answer 12

simplify

Answer 13

thank you :)

Answer 14

u wlc ^_^