In this problem, consider the curve y = f(x) = x²-7x +1. (a) For any real number a, the formula for f' (a) = -2a+7 (b) The equation of the tangent line to the curve y=f(x) at the point P=(a,f(a)) is y=2a-7 x+1-a2 (c) There are two tangent lines to the curve y=f(x) with x-intercept 8. The x-coordinates of these two points of tangency (listed left to right) are: and

A duck's flight is given by the following expression: y = x^2 + x + 4. X and y are coordinates of its flight. When x = 2, the duck takes a hit and thereafter its flight follows the trajectory of a tangent line. What is the coordinate when x=4.

For f(x)=2x-4x2 +8 find the following. (A) f'(x) (B) The slope of the graph off at x= -2 (C) The equation of the tangent line at x= -2 (D) The value(s) of x where the tangent line is horizontal (A) f'(x) = ] (B) At x= -2, the slope of the graph of f is. tent (C) At x = - 2, the equation of the tangent line is y= |. (D) The tangent line is horizontal at x =. (Use a comma to separate answers as needed.) cess Cess ibr lon sou Enter your answer in each of the answer boxes.

Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3, 2); then find the equation of the tangent line corresponding to the smaller x-value.