Question

find the equation of the tangent line to the graph of f at the indicated value of x.
f(x)=3-4lnx; x=1

Answer 1

yes it is

Answer 2

ok

Answer 3

but i have an answer it says its is y=-4x+7 but i dont know how to find the answer

Answer 4

and it would actually simplify to y=3

Answer 5

Ok. Got it. Put x=1 in equation. U'l get y=3.
Differentiate the equation f(x) = 3-4lnx
That gives -4/x, which gives a gradient of -4 at x=1
Apply y = mx +c where m = -4, x=1, y = 3...find c and u have the answer....

Answer 6

but how do they get +7 as the y intercept

Answer 7

it would be 3=-4x+0

Answer 8

c is the y intercept. Put the coordinates and gradient int he equation so it becomes 3 = -4(1) + c so c=7. Rewriting general equation is y = -4x + 7

Answer 9

i understand that but where does the 7 come from

Answer 10

This is a basic linear equations question. You have a linear equation of general form y = mx+ c where you need the values of m and c to specify the equation. m is the gradient and c is the y intercept. so you already have m =-4. To get c, you use the value of m and the coordinates you found earlier i.e. (1,3) . Find c. Write y = mx+ c, plugging in the values of m and c

Answer 11

oh lol i feel stupid thanks