assigment 4 and Webwork 2.4-2.6

WRITTEN ASSIGNMENT 4: MORE DERIVATIVES

CALCULUS I, FALL 2022 MATH 1210-090

INSTRUCTOR: WILL FELDMAN

Name: uID:

Problem 1. Consider the function f(x) = 4 sin(3x + 1).

(a) Find f ′(x).

(b) Find f ′′(x).

(c) Find f (30)(x), the thirtieth derivative of f(x). Hint: Don’t actu- ally compute all those derivatives, compute a few and try to find a pattern.

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2 CALCULUS I, FALL 2022 MATH 1210-090 INSTRUCTOR: WILL FELDMAN

Problem 2. Find the equation of the tangent line to the graph of the function f(x) = 5x

1+3x3 at the point (2, 25).

Problem 3. A ball is thrown directly upward from a height 10 meters above the ground at time t = 0 (seconds). The location y(t) (in meters above the ground) of the ball at time t > 0 is given by

y(t) = −2t2 + t + 10.

(a) Find the velocity of the object at time t.

(b) Find the acceleration of the object at time t.

(c) Find the velocity of the ball at the time when it hits the ground, i.e. the time t∗ > 0 when y(t∗) = 0. Hint: You could use the quadratic formula to find the value of t∗.