Question

The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c – 1, e^{c– 1}), (c + 1, e^c+1)

(a) on the left of x = c

(b) on the right of x = c

(c) at no point

(d) at all points.

Answer 1

Correct option (a) on the left of x = c   

Explanation: 

Given curve is y = e^x

⇒ dy/dx = e^x

Equation of the tangent to the curve at (c, e^c) is

y – e^c = e^c(x – c) ...(i)

Equation of the line joining

Thus, two lines meet on the left of x = c