Question

Use the graph of y=f(x) in the accompanying figure to estimate the value of f′(1).



Estimate of f′(1):

Answer 1

@dan815 @ganeshie8

Answer 2

so to find the first derivative, you find the gradient of the tangent drawn at the point x=1

Answer 3

remember gradient = (y1-y2)/(x1-x2), where (x1,y1) and (x2, y2) are arbitrary points on the tangent.

Answer 4

what do you mean arbitrary

Answer 5

@physo

Answer 6

@dan815

Answer 7

i mean take any 2 points on the line

Answer 8

which line the curve or red line

Answer 9

read off two points from the red line and find the gradient by plugging into the above formula

Answer 10

ok

Answer 11

because red line is a tangent to the curve at the point x=1, which is what we need

Answer 12

lets do (2,6) and (1,2)

Answer 13

slope = 4

Answer 14

how exactly did you get 4?

Answer 15

slope formula

Answer 16

do you understand why the formula works?

Answer 17

yeah because its the slope of the line that is also equal to the curve gradient

Answer 18

its correct, im just making sure you understood what you did

Answer 19

okay so is that all i need to do?

Answer 20

yes

Answer 21

that was correct :D