Question

Show that the line x/a + y/b = 1, touches the curve y = b . e^-x/a at the point where the curve intersects the axis of y.

Answer 1

Given: equation of line x/a + y/b = 1, the curve y = b.e x/a  intersects the y-axis

To show: the line touches the curve at the point where the curve intersects the axis of y

Explanation: given the curve y = b.e x/a intersects the y-axis, i.e., at x = 0

Now differentiate the given curve equation with respect to x, i.e.,

Now substitute x = 0, we get

We will differentiate this with respect to x, we get

Line touches the curve if there slopes are equal.

From equation (i) and (ii), we see that

m₁ = m₂

Hence the line touches the curve at the point where the curve intersects the axis of y.