Area under a tangent line

Forum for the GRE subject test in mathematics.
StarKid
Posts: 4
Joined: Wed Mar 02, 2011 7:45 pm

Area under a tangent line

Postby StarKid » 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?

StarKid
Posts: 4
Joined: Wed Mar 02, 2011 7:45 pm

Re: Area under a tangent line

Postby StarKid » Sat Mar 05, 2011 4:36 pm

Whoops, nevermind. I just realized that I miscalculated the slope; it should be y'(0). What a ridiculous mistake.




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