Question

# Answer each of the questions below. (a) Find an equation for the tangent line to the...

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

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