Find the equation of the tangent line to the curve at the point . The equation of this tangent line can be written in
the form . Find and .

Note: You can earn partial credit on this problem.

Ask by Wright Mills. in the United States

Jan 19,2025

Question

Find the equation of the tangent line to the curve at the point . The equation of this tangent line can be written in
the form . Find and .

Note: You can earn partial credit on this problem.

Ask by Wright Mills. in the United States

Jan 19,2025

UpStudy AI · Accepted Answer

To find the equation of the tangent line to the curve $$ y = 15x e^{2} $$ at the point $$ (0,0) $$, let's analyze the given function.

1. **Understanding the Function:**
   The function $$ y = 15x e^{2} $$ is a linear equation because it can be written in the form $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept. Here, $$ e^{2} $$ is a constant.

2. **Identifying the Slope ($$ m $$) and Y-Intercept ($$ b $$):**
   - **Slope ($$ m $$):** The coefficient of $$ x $$ is $$ 15e^{2} $$, so $$ m = 15e^{2} $$.
   - **Y-Intercept ($$ b $$):** When $$ x = 0 $$, $$ y = 0 $$. Therefore, $$ b = 0 $$.

3. **Conclusion:**
   Since the given curve is a straight line, the tangent line at any point on the curve is the line itself.

**Final Answer:**
$$
m = 15 e^{2}
$$
$$
b = 0
$$
$$ m = 15e^{2} $$ $$ b = 0 $$

Find the equation of the tangent line to the curve at the point . The equation of this tangent line can be written in
the form . Find and .

Note: You can earn partial credit on this problem.

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Find the equation of the tangent line to the curve at the point . The equation of this tangent line can be written in the form . Find and . Note: You can earn partial credit on this problem.

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Find the equation of the tangent line to the curve at the point . The equation of this tangent line can be written in
the form . Find and .

Note: You can earn partial credit on this problem.