For f(x)=3x^2+9x+8 find the equation of the tangent line at the following values of x. (a) x=1 The equation of the tangent line at x=1 is square (b) x=-1 The equation of the tangent line at x=-1 is square

To find the equation of the tangent line to the function at a given value of , we need to find the derivative of the function and then evaluate it at the given value of to find the slope of the tangent line. Finally, we can use the point-slope form of a linear equation to find the equation of the tangent line.Let's start with part (a) where .Step 1: Find the derivative of the function .The derivative of is given by: Step 2: Evaluate the derivative at to find the slope of the tangent line. Step 3: Use the point-slope form of a linear equation to find the equation of the tangent line.The point-slope form of a linear equation is given by: where is the slope of the line and is a point on the line.In this case, the slope of the tangent line is , and we can choose the point on the line. So, the equation of the tangent line at is: Step 4: Substitute the value of into the equation. So, the equation of the tangent line at is: Simplifying the equation, we get: Therefore, the equation of the tangent line at is .Now let's move on to part (b) where .Step 1: Find the derivative of the function .The derivative of is given by: Step 2: Evaluate the derivative at to find the slope of the tangent line. Step 3: Use the point-slope form of a linear equation to find the equation of the tangent line.The point-slope form of a linear equation is given by: where is the slope of the line and is a point on the line.In this case, the slope of the tangent line is , and we can choose the point on the line. So, the equation of the tangent line at is: Step 4: Substitute the value of into the equation. So, the equation of the tangent line at is: Simplifying the equation, we get: Therefore, the equation of the tangent line at is .