The goal of this problem is to compute the value of the derivative at a point for several different functions, where for each one we do so in three different ways, and then to compare the results to see that each produces the same value. For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. Note: At least one graph will have a derivative that does not exist so please enter DNE ƒ(x) = x² − 6x, a = 4 f(x) f(x) = f(x) = 1 = x " a = - 4 Note: the lim sin(x), a = π 2 sin (h) h h→0 √x, a = 1 Hint = 1 and the lim 1 h→0 f(x) = 7 x − 4|, a = 4 cos(h) h = 0

Lexi hiked 3 miles down into the hill at 3 miles per hour, then 3 miles back out of the hill at 1 mile per hour. how to a distance-time graph.   What is the average speed?

The vancouver real estate market has slowed in the last 2 years. A condo valued at 420,000 has lost 18% of its value. Find the loss in value

Rattan enjoys the outdoors.He can bike 5 times faster than he can jog. To cover 20km path, Rayyan needs 2 hours more of he jogs than if he bikes. What is the average speed in km/h on a bike? Round your answer to the nearest tenth if necessary.