please just check to see if i got the right answer! a tangent drawn to y=-(x^2 -4) at the point (1, 3) forms a right triangle with the coordinate axes. find the area of this right triangle. please help!

Question

mathmate · Answer

What is your answer?

anonymous · Answer

oh sorry i said that the area is 16

mathmate · Answer

f(x)=-(x^2-4)
f'(x)=-2x
at (1,3), the tangent line is:
y=-2(x-1)+3=-2x+5
the x-intercept is 5/2, and the y-intercept is 5
So the area is (5/2)(5) / 2 = 25/4