The tangent line to the graph of \( f(x) \) at \( x = 1 \) is shown. On the tangent line, \( P \) is the point of tangency and \( A \) is another point on the line.**Graph Description:**- The graph includes a curve representing the function \( y = f(x) \) and a tangent line intersecting the curve at \( x = 1 \).- The curve starts from the top left of the graph, dips downward, and then curves upward as it moves right across the grid.- The tangent line is a straight blue line angled downward from left to right, passing through the point \( P \) where it touches the curve, and extending past \( A \).**Axes Details:**- The horizontal axis (x-axis) ranges from approximately -4 to 6.- The vertical axis (y-axis) ranges from approximately -5 to 5.- Both axes are marked with integer increments.Points on the Graph:- \( P \) is the point of tangency where the tangent line just touches the curve. It is marked close to \( x = 1 \).- \( A \) is another point on the tangent line, marked near \( x = -3 \).**Tasks:**(a) Find the coordinates of the points \( P \) and \( A \).\( P(x, y) = \left( \text{\_\_ , \_\_} \right) \)\( A(x, y) = \left( \text{\_\_ , \_\_} \right) \)(b) Use the coordinates of \( P \) and \( A \) to find the slope of the tangent line. (Give an exact answer. Do not round.)\(\_\_\_ \)(c) Find \( f'(1) \). (Give an exact answer. Do not round.)\(\_\_\_ \)(d) Find the instantaneous rate of change of \( f(x) \) at \( P \). (Give an exact answer. Do not round.)\(\_\_\_ \)

Note: There are many subparts in the question. So I will answer first three of them and other subparts send separately. Given: the tangent line to the graph of f(x) at x=1 and P is the point of tangency and A is another point on the tangent line. a) The coordinates of the points: P(x, y)=(1, 0) A(x, y)=(-1,1)b) Now the slope of the line is: If we have x1,y1 and x2,y2 then the slope of the line is: m=y2-y1x2-x1 We have, P(x, y)=(1, 0) and A(x, y)=(-1,1) Then the slope of the tangent line is: m=1-0-1-1=1-2 Hence, the slope of the tangent line is -12 c) The slope of the tangent line of the curve y=f(x) at x=1 gives the derivative of the curve that is f'(x) at x=1 Hence, f'(1)=-12