Final answer:
To find the equation of the tangent to the curve y = 2x² - 1 at the point where x = a, you can find the slope of the tangent line using the derivative. The equation of the tangent line can be written in the form 4ax - y = 2a² + 1.
Step-by-step explanation:
To find the equation of the tangent to the curve y = 2x² - 1 at the point (a, 2a² - 1), we need to find the slope of the tangent line at that point. The slope of a curve at a given point can be found using the derivative. So, let's first take the derivative of y = 2x² - 1 with respect to x:
y' = 4x
Now, substitute the x-coordinate a into the derivative to find the slope at the point (a, 2a² - 1):
slope = 4a
Now, we have the slope and a point (a, 2a² - 1). We can use the point-slope form of a linear equation to find the equation of the tangent line:
y - (2a² - 1) = 4a(x - a)
Simplifying this equation gives us:
4ax - y = 2a² + 1