In the following problem:
Consider the set of all triangles whose sides are the x and y axes and tangents to the curve e^{-4 x}, x>0. Calculate the maximum area such a triangle can have.
I have tried to solve it, but the answer is apparently wrong, what have I missed?
y = e⁻⁴ˣ ⟹ dy/dx = -4e⁻⁴ˣ = -1 ⟹
x = (1/2)*ln(0.25) = 0.3465 & y = 0.2501
plug into y = -x+c to find c = 0.5966 both x & y intercept.
area triangle is (0.5966)²/2 = 0.178 units² Answer