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
0
(x).
(b) Find f
00(x).
(c) Find f
(30)(x), the thirtieth derivative of f(x). Hint: Don’t actually compute all those derivatives, compute a few and try to find a
pattern.
1
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+3×3 at the point (2,
2
5
).
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) = −2t
2 + 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∗.
