To find f'(1), take the derivative of the given function f(x) = 2eˣ - 6x and substitute x = 1 into the derivative. The value of f'(1) represents the slope of the tangent line to the curve at the point (1, f(1)).
To find f'(1), we need to take the derivative of the function f(x) = 2eˣ - 6x.
The derivative of eˣ is eˣ and the derivative of constant -6x is -6. So, the derivative of f(x) is f'(x) = 2eˣ - 6.
To find f'(1), we substitute x = 1 into the derivative function: f'(1) = 2e¹ - 6.
Evaluating this expression gives f'(1) ≈ -0.28.
The value of f'(1) represents the slope of the tangent line to the curve of f(x) at the point (1, f(1)).