What is the equation of the line tangent to #f(x)=4x^3+12x^2+9x+7# at #x=-3#?
1 Answer
Explanation:
We can find the slope of a line tangent to a curve at a point by evaluating the derivative of the function at that point.
We are given the function
Using the power rule, let's now compute the derivative of
We can now find the slope of
Now that we have a slope for the tangent line, we need to identify a point on the line.
We know the tangent line touches the function
So we know the tangent line goes through the point
Finally, we can use the point-slope formula for a line to find the equation of the tangent line.
To find the value of
So our final answer for the equation of the tangent line is: