Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct.

Question

Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. ​  ​

Quizplus · Accepted Answer

First, we need to find the derivative of the function:
f'(x) = -2x - 3
Next, we need to find the slope of the tangent line by plugging in the x-value of the given point:
f'(-2) = -2(-2) - 3 = 1
So, the slope of the tangent line is 1.
Finally, we can use the point-slope form of a line to find the equation of the tangent line:
y - (-1) = 1(x - (-2))
y + 1 = x + 2
y = x + 1

We can graph both the function and the tangent line to check our work. The function is a parabola opening downwards and the tangent line intersects the function at (-2,-4). The graph confirms that our choice of B is correct.

Write the Equation of the Line Tangent to the Graph