Question

Consider the following curve.

y = √7- 2x
Find the slope m of the tangent line at the point (-1, 3).
m =____
Find an equation of the tangent line to the curve at the point (-1, 3).
y =_______

Answer 1

To find the slope of the tangent line at the point (-1, 3), we need to find the derivative of the given curve. The derivative of y = √(7 - 2x) can be found using the chain rule and is given by dy/dx = (-2/2)√(7 - 2x). Evaluating this derivative at x = -1 gives us the slope of the tangent line at the point (-1, 3). The equation of the tangent line at the point (-1, 3) is y = -x + 2.

Step-by-step explanation:

To find the slope of the tangent line at the point (-1, 3), we need to find the derivative of the given curve. The derivative of y = √(7 - 2x) can be found using the chain rule and is given by dy/dx = (-2/2)√(7 - 2x). Evaluating this derivative at x = -1 gives us the slope of the tangent line at the point (-1, 3).

Substituting x = -1 into the equation of the curve, we can find the corresponding y-coordinate. y = √(7 - 2(-1)) = √(9) = 3. Therefore, the equation of the tangent line at the point (-1, 3) is y - 3 = m(x + 1), where m is the slope we calculated earlier. Plugging in the slope, the equation becomes y - 3 = (-2/2)(x + 1), which simplifies to y = -x + 2.