Tangents and Normals

[izzzy223]

Find the coordinates of point S where the tangent to the curve y = x^2 + 4x – 1 is perpendicular to the line 4x + 2y + 7 = 0.

 

[Deleted member 4993]

Find the coordinates of point S where the tangent to the curve y = x^2 + 4x – 1 is perpendicular to the line 4x + 2y + 7 = 0.

What would be the slope of the tangent line to the curve at (x₁,y₁)?

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[HallsofIvy]

Where did you get this problem? Do you know what "tangent" and "normal" mean? Do you know what the "slope of a line" is? If so what is the slope of the line given by 4x+ 2y+ 7= 0? What is the slope of the line tangent to the graph of y= f(x) at \(\displaystyle (x_0, f(x_0)\)? What is the relationship between slopes of two lines that are normal to each other? You need to be able to answer those questions to do this problem. If you can't, get out your textbook and review!

 

[pka]

Find the coordinates of point S where the tangent to the curve y = x^2 + 4x – 1 is perpendicular to the line 4x + 2y + 7 = 0.

In your precalculus courses you should have learned that ax+by+d=0 is a line and if \(a\cdot b\ne 0\) then its slope is \(\dfrac{-b}{a}\).
Moreover the line is perpendicular to any line that has a slope of \(\dfrac{a}{b}\).
Where on the parabola \(y=x^2+4x-1\) does the its slope equal that which is perpendicular to the line \(4x+2y+7=0~?\)

 

[izzzy223]

In your precalculus courses you should have learned that ax+by+d=0 is a line and if \(a\cdot b\ne 0\) then its slope is \(\dfrac{-b}{a}\).
Moreover the line is perpendicular to any line that has a slope of \(\dfrac{a}{b}\).
Where on the parabola \(y=x^2+4x-1\) does the its slope equal that which is perpendicular to the line \(4x+2y+7=0~?\)

Thank you so much!!!