The original function is given, y = 2 x 2 + 2 x + 7at the point ( 4 , 47 ).I found the tangent line from the original function which is: f ′ ( x ) = 4 x + 2.The question states that the tangent line can be written as y = m x + b and asks me to find the slope ( m) as well as the y-intercept ( b).I have found the slope which is 18, by plugging in the x-value from the point ( 4 , 47 ) into the tangent line: so I have f ( x ) = 4 x + 2 which equals 4 ( 4 ) + 2 which is 18.The way I'm trying to find the y-intercept is by doing: y − 47 = 18 ( x − 3 ) which is − 7, but it's wrong the answer is − 25.What mistake am I making that's leading me to get − 7?

Question

The original function is given,  y  =  2      x    2    +  2  x  +  7at the point   (  4  ,  47  ).I found the tangent line from the original function which is:      f    ′    (  x  )  =  4  x  +  2.The question states that the tangent line can be written as   y  =  m  x  +  b and asks me to find the slope (  m) as well as the   y-intercept (  b).I have found the slope which is   18, by plugging in the   x-value from the point   (  4  ,  47  ) into the tangent line: so I have   f  (  x  )  =  4  x  +  2 which equals   4  (  4  )  +  2 which is   18.The way I&#039;m trying to find the   y-intercept is by doing:   y  −  47  =  18  (  x  −  3  ) which is   −  7, but it&#039;s wrong the answer is   −  25.What mistake am I making that&#039;s leading me to get   −  7?

kpgt1z · Accepted Answer

Instead of   y  −  47  =  18  (  x  −  3  ), you should say   y  −      47    =  18  (  x  −      4    ), because the point   (      4    ,      47    ) is on the tangent line, and then you&#039;ll get the correct answer.

enrotlavaec · Accepted Answer

You&#039;re making a mistake at this part :  x  −  3it should be  x  −  4You can also use   y  =  m  x  +  c instead of the complicated   y  −  y  1  =  m  (  x  −  x  1  ). Because you already know   m and a point   (  4  ,  47  ) then you just need to find   c, that way is gonna be easier and will make you avoid calculation mistake

The original function is given, y = 2 x 2 </msup> + 2 x + 7 at the

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