Question

Consider the function f(x)=x^2+5x+2 and the point A(4,2).
f′(x)=........
Find a formula for the slope of a line passing through point A, and an arbitrary point on the function. Your answer should be a formula in terms of x.
slope=.........
Using your answers from the two previous questions, find the slope(s) of the line(s) through point A that is (are) tangent to f(x). If there is more than one line you can separate your answers with a comma (ex. 5,2 ).
slope(s)=

Answer 1

Find the derivative of f(x), then use the 4 or "x" from the point A and use it as the input of the derivative. So, f'(4)=.... That will yield your slope. Then use the point intercept form to find the tangent line y-y1=m(x-x1) Or do you need help finding the derivative?

Answer 2

so f(x)= 2x+5 and f'(4)=13? how do i get the slope out of this?

Answer 3

The derivative is directly related to slope. It is the slope of the tangent line.
So f'(x)=2x+5, f'(x)=13. Now use point slope form y-y1=m(x-x1)
y-2=13(x-4)

Answer 4

The derivative yields the tangent slope. So f'(x)=slope of f(x)

Answer 5

so slope is 13(x-4)+2=26x-104? what about the last part?

Answer 6

the derivative of any function gives you the slope of that function ie (dy/dx)=tan theta

Answer 7

basically slope at any point of the curve is equal to the derivative wrt x at that point

Answer 8

so dy/dx = 2x +5 and at the point (4,2) it will become 13 then use the line equation formula

Answer 9

the slope of 13 is INCORRECT

Answer 10

that is the second blank

Answer 11

take any point on the curve as (x , x^2 + 5x + 2) then the slope will be equal to \[m = \frac{ x^2 + 5x +2 - 2 }{ x -4 } = \frac{ x^2 + 5x }{ x -4 }\]

Answer 12

katie is this correct?

Answer 13

let me check suvesh

Answer 14

thats also incorrect

Answer 15

but that should be correct because i have directly used the formula for slope of a line between 2 points

Answer 16

suvesh did i type it correctly? please check in the attachment.

Answer 17

no just type the last part
means x^2 + 5x / x -4 part only

Answer 18

YES!! survesh that was correct

Answer 19

do you how to do the last blank?

Answer 20

answers for the last one is 10,-2

Answer 21

you just have to solve
\[\frac{ x^2 + 5x }{ x - 4} = 2 x + 5\]
you will get a quadratic whose roots are 10, -2

Answer 22

when i type the answer in, it says i need to evaluate f'(x) at these points

Answer 23

how do i do that?

Answer 24

ok then this is the x-value you have got
derivative of f(x) = 2 x +5
answers will be (2 x 10 + 5) and (2 x -2 +5) = 25 and 1

Answer 25

\[f \prime(x) = 2 x +5 \]

Answer 26

yes!! you got it again. thank you very much suvesh

Answer 27

do you know how to do cost function questions?

Answer 28

nope sorry katie

Answer 29

no worries. thankyou anyway. see you around. bii

Answer 30

bye