Use formulas (1) and (2) and the power rule to find the derivatives of the following functions. f ( x ) = 1 x 3 . Derivative of Linear Function If f ( x ) = m x + b , then we have f ' ( x ) = m . ( 1 ) Constant Rule The derivative of a constant function f ( x ) = b is zero. That is, f ' ( x ) = 0 . ( 2 ) Power Rule Let r be any number, and let f ( x ) = x r . Then f ' ( x ) = r x r − 1 .
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions. f ( x ) = 1 x 3 . Derivative of Linear Function If f ( x ) = m x + b , then we have f ' ( x ) = m . ( 1 ) Constant Rule The derivative of a constant function f ( x ) = b is zero. That is, f ' ( x ) = 0 . ( 2 ) Power Rule Let r be any number, and let f ( x ) = x r . Then f ' ( x ) = r x r − 1 .
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY