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 and show all steps!

Question

turingtest · Answer

find f'(1) to find the slope of the function at (1,3)
then us that value in point-slope form$$y-y_0=f'(x_0)(x-x_0)$$

turingtest · Answer

that will allow you to fins the intercepts of the line with the coordinate axis, which gives you the length of the sides of the triangle.

anonymous · Answer

okay so is the slope -2?

turingtest · Answer

yes
f'(1)=-2

anonymous · Answer

okay so then is the area 16?

turingtest · Answer

I'm not sure, I haven't tried it, give me a minute...

turingtest · Answer

I got 25/4
what did you get for the intercepts?

turingtest · Answer

I got
y-3=-2(x-1)
y=-2x+5
x-int=5/2
y-int=5
area=[(5/2)*5]/2=25/4

anonymous · Answer

okay that makes sense thank you!