anonymous
  • anonymous
Find an equation for a line that is tangent to f(x)=x^2-2x-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
for any point? or do you want a formula for any point?
anonymous
  • anonymous
it doesn't specify, it just says to find an equation.
myininaya
  • myininaya
ok say we want to find the tangent line at x=a

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myininaya
  • myininaya
f'(x)=2x-2
myininaya
  • myininaya
so the slope at x=a is f'(a)=2a-2
myininaya
  • myininaya
a line has the form y=mx+b
myininaya
  • myininaya
we know the slope m is 2a-2
myininaya
  • myininaya
so now we have y=(2a-2)x+b we now need to find the y-intercept
myininaya
  • myininaya
we know a point on this line (a,f(a))
myininaya
  • myininaya
f(a)=a^2-2(a)-3
myininaya
  • myininaya
a^2-2a-3=(2a-2)a+b
myininaya
  • myininaya
so we now solve this for b to find the y intercept
myininaya
  • myininaya
so we have y=(2a-2)x-a^2-3
myininaya
  • myininaya
this is the general equation for the tangent line at (a,f(a))
anonymous
  • anonymous
you think i can just pick a point off the original quadratic function and use those points, such as the point (3,0)?
myininaya
  • myininaya
It does say to find *an* so maybe it doesn't matter, but make sure the point is on the curve ( I mean verify that it is) Does f(3)=0?
anonymous
  • anonymous
since a point was not specified in the original problem and yes, f(3)=0.
myininaya
  • myininaya
ok you can use this point as long as we aren't looking for anything general.
anonymous
  • anonymous
ok thanks so much, i don't need to find the x and y intercepts right?
myininaya
  • myininaya
no. you can just use the general tangent line that I came up with. lol
myininaya
  • myininaya
but your teacher will probably want you to show work
anonymous
  • anonymous
ok thanks so much for your help :)

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