The equation of the tangent line to $f ( x ) = 3 e ^ { x }$ at x = 0 is y = 3x + 3.

Name: The equation of the tangent line to $f ( x ) = 3 e ^ { x }$ at x = 0 is y = 3x + 3.
Brand: Quizplus
Rating: 5.0 (43 reviews)

Question

Quizplus · Accepted Answer

The derivative of $f(x) = 3e^x$ is $f'(x) = 3e^x$, and at $x = 0$, $f'(0) = 3$. The value of the function at $x = 0$ is $f(0) = 3$. Therefore, the equation of the tangent line at $x = 0$ is $y = 3x + 3$, using the point-slope form $y - y_1 = m(x - x_1)$, where $m = 3$ and $x_1 = 0$, $y_1 = 3$.

The Equation of the Tangent Line To f(x)=3exf ( x ) = 3 e ^ { x }f(x)=3ex

The Equation of the Tangent Line To $f ( x ) = 3 e ^ { x }$