Question

Consider the following function and point. See Example 10.f(x)=(6 x+1)² ; quad(0,1)

a. Find an equation of the tangent line to the graph of the function at the given point.y=

Answer 1

To find the equation of the tangent line to the graph of the function f(x) = (6x+1)² at the point (0,1), we need to find the slope of the tangent line at that point. The slope of a tangent line can be found by taking the derivative of the function.

Step-by-step explanation:

To find the equation of the tangent line to the graph of the function f(x) = (6x+1)² at the point (0,1), we need to find the slope of the tangent line at that point.

The slope of a tangent line can be found by taking the derivative of the function. In this case, the derivative of f(x) = (6x+1)² is f'(x) = 12(6x+1).

Since we want the slope at the point (0,1), we can substitute x = 0 into the derivative to get f'(0) = 12(6(0)+1) = 12.

So the equation of the tangent line is y - 1 = 12(x - 0), which simplifies to y - 1 = 12x.