Draw the tangent lines at x = -2, -1, 0, 1, and 2 on the graph of y = f(x). Estimate the values of f' (-2), f'(-1), f' (0), f' (1), and f' (2) and list the values in the table provided. f' (z) -2 Based on your estimate values of f' (x ) at a = -2, -1, 0, 1, and 2, find a linear equation for f' (a). f' (z) =(1 point) The image below shows the graph of the function f[:c). answer the following (all intervals should be inside the bigger interval (7, 7); do not include Using what you know about the derivative function any points in your intervals outside of this set}: a) When does f'(:r:) cross the iii-axis? . b) When is f'(m) 2 0? c) When is f'(a:) g 0? '- (1 point) Consider the graph of ax) below. For the following questions, if a value does not eartist1 writ: o.) What is the value of f'(1)? I 55! b) What is the value of f'(1)? I 555 . c) What is the value of fff)? EEE (1 point) To help with this problem, you may assume that the derivative of a sum of differentiable functions is the sum of the derivatives. a) Find a second degree polynomial m) such that f(0) = 7, f'(0) = 0, and f"(0) = 4. x) 2 I as: 5) Find a second degree polynomial 9(3) such that 9(0) 2 6, g'(0) = 7, and 9"(0) = 9. 9(3) 2 I ::: (1 point) Again, to help with this problem you may assume that the derivative of a sum of differentiable functions is the sum of the derivatives. Does the parabola y = 3x+ 2x - 5 have a tangent whose slope is 7? If so, find an equation for the line and the point of tangency. If not, enter DNE into both boxes. Tangent Line: y = Point of Tangency:(1 point) In January 2010, Business B in Omaha earned one dollar in revenue from sales every 9 seconds. Business B also earned one dollar in revenue from investments every 30 seconds. Finally, Business B spent one dollar in expenses every 20 seconds. a) Let P(t) be the total profit earned by Business B, where t is the time in seconds measured from the start of January 2010. Find P'({]), and give units. P' (0) 2 555 555 per === b) To the nearest second, how long did it take for Business B to earn one dollar of profit? Time to rst dollar: 555 seconds