Final answer:
To find the equation of the tangent line to the curve y = 6ex at the point (0, 6), find the derivative of the function, substitute x=0, and use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of the tangent line to the curve y = 6ex at the point (0, 6), we need to find the slope of the curve at that point and then use the point-slope form of a linear equation. The slope of the curve at a point is given by the derivative of the function. Taking the derivative of y = 6ex with respect to x gives us dy/dx = 6e^x. Substituting x=0 into the derivative, we get dy/dx = 6e^0 = 6. Therefore, the slope of the tangent line is 6.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), we can plug in the coordinates of the given point (0, 6) and the slope 6 to find the equation of the tangent line. Therefore, the equation of the tangent line is y - 6 = 6(x - 0), which simplifies to y = 6x + 6.