Calculus I, Fall 2015 (http://www.math.nthu.edu.tw/˜ wangwc/)

Brief answer to selected problems in HW08

1. Section 4.2: problem 17(b): The new polynomial is the derivative of the original polynomial. Apply Rolle’s Theorem to the original polynomial. problem 18: Apply Rolle’s Theorem to f, then to f′. problem 65: Apply mean value theorem to f on [0, x]. problem 66: Apply mean value theorem to sin(x) on [a, b].

2. Section 4.3: problem 74: Solve for a, b, c, d from f(0) = 0, f(1) = −1, f′(0) = 0 and f′(1) = 0. problem 80: (a): Show that f(x) = e^{x} −(1+x) satisfies f(0) = 0 and f is increasing on x ≥ 0. (b): Show that g(x) = e^{x} − (1 + x + x^{2}/2) satisfies g(0) = 0 and g is increasing on x ≥ 0 using the result in (a).