94 3. LIMITS, DERIVATIVES, RULES, AND THE MEANING OF THE DERIVATIVE
that has y D 3x C 2 as a tangent line. Demonstrate that your answer is correct.
2
-1
-4 4
g(x)
Problem 3.34 For the function g.x/ shown above, find the interval(s) on which tangent lines
have negative slopes and the interval(s) on which tangent lines have positive slopes.
Problem 3.35 Find all tangent lines to the function h.x/ D x
4
4x that have slope m D 1.
Problem 3.36 Suppose that
r.x/ D ax
3
C bx
2
C cx C d:
en what is the largest number of tangent lines that r.x/ can possess that have the same slope?
Problem 3.37 Find a polynomial with no roots whose first derivative has three roots.
Problem 3.38 Suppose that s.x/ is a quadratic polynomial. What is the geometric interpreta-
tion of the point .x; s.c// where s
0
.c/ D 0.
3.3 DERIVATIVES OF THE LIBRARY OF FUNCTIONS
is section is a catalog of the derivatives of the library of functions. It also introduces three
new functions: the inverses of the sine, tangent, and secant functions. We can already take the
derivative of polynomial functions using combinations of powers of x. It turns out that the rule
for powers of the form x
n
also applies for powers that are not whole numbers.
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.