Linear approximation Find the linear approximation to the following functions at the given point a.


f(x) = 4x² + x; a = 1

Verified step by step guidance

1. Identify the function f(x) = 4x² + x and the point a = 1 where we want to find the linear approximation.
2. Calculate the derivative of the function f(x) to find f'(x). The derivative will help us determine the slope of the tangent line at the point a.
3. Evaluate the derivative at the point a = 1 to find the slope of the tangent line, which is f'(1).
4. Calculate the value of the function at the point a = 1, which is f(1). This will give us the y-coordinate of the point on the curve.
5. Use the point-slope form of the equation of a line, y - f(a) = f'(a)(x - a), to write the linear approximation L(x) around the point a.