The slope of the tangent to a curve C: y = y(x) at any point (x, y)

The slope of the tangent to a curve C: y = y(x) at any point (x, y) on it is . If C passes through the points and

Then is equal to

1. 
2. 
3. 
4. 

Solution:

Tip for solving this question:

Use the formula of the slope of the tangent.

On integration, find the value of y.

Then using points find

Step 1 of 3:

As we know, slope of tangent =

Given, Slope of tangent =

……….(1)

Step 2 of 3:

Now, integrate equation (1)

$latex\int {dy = \int {{e^{2x}} – \frac{{6{e^{ – x}}}}{{2 + 9{e^{ – 2x}}}}dx} } $

.

Step 3 of 3:

If satisfies the curve then, we get

Also, If satisfies the curve then, we get

Final Answer:

Hence, Option (B) is correct.