SOLUTION: Please can you answer this question Find the equation of the tangent of the curve y=x^4-x+1 at the point with x Coordinates 1 thankyou

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Question 826996: Please can you answer this question
Find the equation of the tangent of the curve y=x^4-x+1 at the point with x
Coordinates 1
thankyou
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
y%22%22=%22%22x%5E4-x%2B1
The graph of that is gotten by plotting

(-2,19), (-1,3), (0,1), (1,1), (2,15) 



The slope of a tangent line at a point IS the derivative
at that point.  So we find %28dy%29%2F%28dx%29

%28dy%29%2F%28dx%29%22%22=%22%224x%5E3-1

Evaluate that at x=1

%22%22=%22%224%281%29%5E3-1%22%22=%22%224-1%22%22=%22%223

Now we find the equation of the line with slope m=3 that
goes through to point where x=1.  We must find the y-coordinate,
by substituting x=1 in the original equation for the graph:

y%22%22=%22%22x%5E4-x%2B1
y%22%22=%22%221%5E4-1%2B1
y%22%22=%22%221

Use the point-slope formula:

y - y1 = m(x - x1)
where (x1,y1) = (1,1)

y-1 = 3(x-1)
y-1 = 3x-3
  y = 3x-2    <---answer

Find the points on that tangent line (0,-2), (1,1), (2,4), (3,7)
and graph it as a check to make sure it looks like it's tangent 
to the curve:




Edwin