Answer
$y = 6x + 1$
Work Step by Step
1. Find the derivative of $f(x)$
$f(x) = e^{6x}$
$f'(x) = 6e^{6x}$
2. Substitute the point (0, 1) into $f'(x)$ to find the gradient of the tangent
$f'(0) = 6e^{6(0)}$
$=6e^{0}$
$m =6$
3. Substitute the coordinates and the slope into the equation of the line
$y = mx + b$
$1 = 6(0) + b$
$1 = 0 + b$
$b = 1$
4. Write the equation of the tangent
$y = 6x + 1$
