Area under a tangent line
Posted: Sat Mar 05, 2011 4:34 pm
This is driving me crazy!
What is the area of the region bounded by the coordinate axes and the line tangent to the graph of $$y=\frac{1}{8}x^{2}+\frac{1}{2}x+1$$ at the point (0,1)?
I differentiated y to get a slope of 1/4. Used the equation of a line and the given point to get the equation of the tangent line: $$y=\frac{1}{4}x+1$$. The line forms a triangle, intersecting the y-axis at y=1 and intersecting the x-axis at x=-4. So, base of length 4, height of length one, the area is half of 4 times 1, which is 2. The given answer is 1.
Am I missed something?
What is the area of the region bounded by the coordinate axes and the line tangent to the graph of $$y=\frac{1}{8}x^{2}+\frac{1}{2}x+1$$ at the point (0,1)?
I differentiated y to get a slope of 1/4. Used the equation of a line and the given point to get the equation of the tangent line: $$y=\frac{1}{4}x+1$$. The line forms a triangle, intersecting the y-axis at y=1 and intersecting the x-axis at x=-4. So, base of length 4, height of length one, the area is half of 4 times 1, which is 2. The given answer is 1.
Am I missed something?