Question

f ' (x) for a given function is (x^2)/(x+3) and we are told that f (6) = 30. Write the equation of the tangent line to f(x) at x = 6 and use the tangent line equation to approximate the value of f (6.02).

29.92

30.02

30.08

34.00

none of these

Answer 1

ok so whats the slope there

Answer 2

are u are given a point this line passes through

Answer 3

No, that's all i was given.

Answer 4

yes you are given enough information

Answer 5

you are given a function that tells you the slope at every x value u want

Answer 6

so what is he slope at x=6?

Answer 7

you are also told that f(6)=30 meaning
this tangent line passes through the point(6,30)

Answer 8

y-yo=m(x-xo)
y-30=f'(6)(x-6)

Answer 9

y=30=4(x-6)

Answer 10

y-30=4(x-6)***

Answer 11

y-30=4x-24

Answer 12

y=4x+6

Answer 13

slope 4

Answer 14

now approximate the value at 6.02

Answer 15

this line gives you a linear approximation

Answer 16

:/ how do i do that. idk the equation for f(x)

Answer 17

its good for values very close to 6

Answer 18

y-30=4(6.02-6)
y=4*0.02 + 30 = 30.08

Answer 19

oh, thanks!