MATH 1300 Study Guide - Midterm Guide: The Tangent, Telephone Numbers In The United Kingdom, Hypotenuse

• School: CU-Boulder
• Department: Mathematics
• Course: MATH 1300
• Professor: All

Document Summary

[1, ) and ( , 2]: let f (x) and g(x) be the functions graphed below. Let h(x) = f (x)g(x), let j(x) = x2f (x), let k(x) = f (x2), let p(x) = f (x)/g(x), let q(x) = f (g(x)), and r(x) = g(g(x)). (a) estimate h(cid:48)(1), h(cid:48)(0), p(cid:48)(0), q(cid:48)(0), r(cid:48)(1), and r(cid:48)(2). Answer: h(cid:48)(1) = 6, h(cid:48)(0) = 0, p(cid:48)(0) = 2, q(cid:48)(0) = 4, r(cid:48)(1) = 0, r(cid:48)(2) = 4. (b) estimate j(cid:48)( 1) and k(cid:48)( 1). Answer: j(cid:48)( 1) = 10 and k(cid:48)( 1) = 4. (c) estimate all values of x for which y = r(x) has a horizontal tangent line. Answer: x = 1, x = 0. 4, x = 2. 4: using the information in the table, nd: Answer: (a) h(4) = 1 (b) h(cid:48)(4) = 2 (c) h(4) = 3 (d) h(cid:48)(4) = 3 (e) h(cid:48)(4) = 5 (f) h(cid:48)(4) = 13. 16: a graph of f (x) is shown below.