A graph of a function f(x) is shown: Using a ruler, carefully draw a tangent line to the function at the point (-1, f(-1)). Then, using the grid provided, find another point on the tangent line you drew. Using the two points at your disposal, compute the slope of the line tangent to the curve at (-1.f(-1)). You have thus estimated the slope of the tangent line at (-1.f(-1)). Repeat this exercise to estimate the slopes of the tangent lines at the points (x,f(x)) where x = 0, 1, 2. Enter all your results in the first three rows of the table below. With f(x) = (x + 2) (x - 1) (x - 3) find the slope of the tangent line algebraically using the definition of the derivative as f'(x) = lim f(x + h) - f(x)/h. Evaluate the derivatives as f'(x) you found at the points x = -1, 0, 1 and 2. Then for each value of x, find the equation of the tangent line using the exact slope and the point of the tangency. Record all your results in the table below. Find the percent error of the estimated slope compared to the actual slope at x = 1.
Show transcribed image text A graph of a function f(x) is shown: Using a ruler, carefully draw a tangent line to the function at the point (-1, f(-1)). Then, using the grid provided, find another point on the tangent line you drew. Using the two points at your disposal, compute the slope of the line tangent to the curve at (-1.f(-1)). You have thus estimated the slope of the tangent line at (-1.f(-1)). Repeat this exercise to estimate the slopes of the tangent lines at the points (x,f(x)) where x = 0, 1, 2. Enter all your results in the first three rows of the table below. With f(x) = (x + 2) (x - 1) (x - 3) find the slope of the tangent line algebraically using the definition of the derivative as f'(x) = lim f(x + h) - f(x)/h. Evaluate the derivatives as f'(x) you found at the points x = -1, 0, 1 and 2. Then for each value of x, find the equation of the tangent line using the exact slope and the point of the tangency. Record all your results in the table below. Find the percent error of the estimated slope compared to the actual slope at x = 1.
