Question

Answer each of the questions below. (a) Find an equation for the tangent line to the graph of y = (2x + 1)(2x 2 − x − 1) at the point where x = 1. (b) Suppose that f(x) is a function with f(130) = 46 and f 0 (130) = 1. Estimate f(125.5). (c) Use linear approximation to approximate √3 8.1 as follows. Let f(x) = √3 x. The equation of the tangent line to f(x) at x = 8 can be written in the form y = mx + b. Compute m and b. Using this find the approximation for √3 8.1. 3. (5 pts) For each of the listed functions, determine a formula for the derivative function. It is important to be comfortable with using letters other than f and x. For example, given a function p(z), we call its derivative p 0 (z). (a) f(x) = x 101 + x − k x (b) g(x) = 8x 12 − 3 7x + π sin(x) − 2 sec(x) (c) p(z) = cos(z)+z sin(z)+z (d) h(t) = (t + 1) sin(t) + t 2 tan(t)+1 (e) c(r) = r 2 csc(r)+13

Answer 1