Recall that the slope m of the graph of f at the point (x, f(x)) is equal to the slope of its tangent line at (x, f(x)), and is given by the following provided this limit exists.m = lim h→0 msec = lim h→0 f(x + h) − f(x)hTherefore, we will first need to find the expression that represents the secant line at the point (2, −10).First, set up the difference equation for the point (2, −10) by substituting x = 2.m  =  lim h→0 f(x + h) − f(x)h =  lim h→0 f  + h − f  h

Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x + 10.What are f(2) and f '(2)?

f(x)=−3x 2 +ax+bFor the quadratic function given above, a and b are constants such the x-coordinate of the vertex is 2.5. If the graph of the function given above is tangential to the line y=10, then find the value of f(3).

Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution.

Find the slope of f(x)𝑓(𝑥) at x=2𝑥=2. The graph of f(x)𝑓(𝑥) is shown below.Move the point on the curve to x=2𝑥=2. Then plot two points on the tangent line. Finally, calculate the slope of f(x)𝑓(𝑥) at x=2𝑥=2. Write your answer as a simplified fraction or rounded to 44 decimal places.

Find the function whose tangent has slope 𝑥 3 − 2 𝑥 2 + 16 for each of x and whose graph passes through the point (2,5).