The tangent to the curve y = e2x at the pointegral (0, 1) me... | MATH - ROLLE'S THEOREM, LAGRANGE'S MEAN VALUE THEOREM | SolveeIt | Solveeit

Today, August 19

Question

The tangent to the curve y = e^2x at the point (0, 1) meets x-axis at the point –

A

(0, 2)

B

(2, 0)

C

(–1/2, 0)

D

(0, –1/2)

Answer

(–1/2, 0)

Explanation

Solution

$\left( \frac{dy}{dx} \right)$ = 2.e^2x Ž $\left( \frac{dy}{dx} \right)_{(0,1)}$ = 2.e⁰ = 2

Ž E.O.T. = (y – 1) = 2.(x – 0)

tangent y = 2x + 1

if meeting at x-axis so

y = 2x + 1 = 0 Ž x = $- \frac{1}{2}$ , y = 0

Point (–1/2, 0)