Question

Let f(1)=−3 and f′(1)=8. Then the equation of the tangent line to the graph of y=f(x) at x=1 is
y=

Answer 1

@dan815

Answer 2

well i Know we have one point (1,-3)

Answer 3

okay but what is the other point?

Answer 4

what else do you need to write the equation of tangent line in "point - slope" form ?

Answer 5

remember the equation of a lien in "point-slope" form ?

Answer 6

y+3=m(1-x)

Answer 7

that is close, try again :

Answer 8

whoops y+3=m(x-1)

Answer 9

Yes, how to find the value of the slope, m ?

Answer 10

derivative gives you the slope

Answer 11

but we know that the derivative of 1 is 8

Answer 12

derivative of a function at a point gives the slope of the tangent line to the graph at that point

Answer 13

so is the slope 8

Answer 14

Yes

Answer 15

simply plugin m=8 in the tangent line eqn that you have got earlier

Answer 16

so the equation is y=8x-5

Answer 17

step by step, please

y+3=m(x-1)

plugin m = 8, what do you get ?

Answer 18

y+3=8(x-1)

Answer 19

you should be able to do the simplification on your own

Answer 20

just work it step by step

Answer 21

whoops i got it silly mistake y=8x-11

Answer 22

looks good

Answer 23

thanks man

Answer 24

Np