Question

Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P. y = 5-7x^2 P(4, - 107)

Answer 1

y = 5 - 7x^2

slope of the curve = derivative of y' = -14x

At the point P(4, -107) the slope is:

y' = -14(4) = -56

a) Answer: Slope at P(4, -107) is -56

b) The equation would be:

y = mx + b where m = -56 and we can calculate b using the point: (4, -107)

b = y - mx = -107 - (-56)(4) = -107 + 224 = 117

b) Answer: Equation of the tangent line at P is

y = -56x + 117