Find the tangent line to the graph of f(x) = sin x + cos x at (π, -1).
A) y = π
B) y = -x + π -1
C) y = x + π
D) y = -x + 1
E) none of these

Question

Quizplus · Accepted Answer

To find the equation of the tangent line at the point (π, -1), we need to find the slope of the tangent line, which is equal to the derivative of the function at that point.

f(x) = sin x + cos x

f'(x) = cos x - sin x

f'(π) = cos π - sin π = -1

So the slope of the tangent line at (π, -1) is -1.

Now we use point-slope form to find the equation of the tangent line:

y - y₁ = m(x - x₁)

where m is the slope, (x₁, y₁) is the point on the graph, and (x, y) is a point on the tangent line.

Plugging in the values we have:

y - (-1) = (-1)(x - π)

Simplifying:

y = -x + π - 1

Therefore, the answer is B, y = -x + π - 1.

Find the Tangent Line to the Graph of F(x) =