Question

Let (−6)=3 and ′(−6)=−3. Then the equation of the

tangent line to the graph of y=(x) at x=−6 is y="

Answer 1

The equation of the tangent line to the graph of y=f(x) at x=−6 is y = -3x - 15.

Step-by-step explanation:

To find the equation of the tangent line to the graph of y=f(x) at x=−6, we need to use the point-slope form of the equation for a line.

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Given that f(−6)=3 and f′(−6)=−3, we know that the point on the tangent line is (-6, 3) and the slope of the tangent line is -3.

Substituting these values into the point-slope form, we get y - 3 = -3(x + 6).

Simplifying the equation gives us y = -3x - 15.

Therefore, the equation of the tangent line to the graph of y=f(x) at x=−6 is y = -3x - 15.