Anonymous A.

asked • 05/22/17

The straight line L

According to the image:http://puu.sh/vYqxg.png
The straight line L is a tangent to the function F at the point C and intersects the X-axis at the point A(-4,0), the coordinates of the point B(4,0) and f(4)+f'(4)=9, then the area of triangle ABC = _____ square unit

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By:

Mark M. answered • 05/22/17

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f(4) / 8 = f'(4)     slope/derivative
f(4) = 8 f'(4)
f(4) + f'(4) = 9    given
f'(4) = 9 - f(4)
f(4) = 8(9 - f(4))  substitution
f(4) = 72 - 8f(4)
9f(4) = 72
f(4) = 8
 
Can you now calculate area?
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Anonymous A.

Yes it would be 0.5 * 8 * 8 = 32 unit length.

But I have two questions...
  1. Did you get this equation "f(4) / 8 = f'(4) slope/derivative" from m=(y2-y1)/(x2-x1) ?
  2. I got all of the answer you wrote mathematically, but on graph isn't f'(4)=f(4) as point C is common point with Function F and Tangent L which is supposed to be the Slope of tangent?

Thank you.
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05/22/17

Mark M.

1.
Δy = f(4), that is f(4) - 0
Δx = 8, that is 4 - (-4)
2.
At C f'(4) is the slope at that point and that slope is f(4)/8, from 1.
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05/22/17

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