Let f ( x ) = x 3 . (a) Estimate the values of f' (0), f ' ( 1 2 ) , . f' (1), f' (2), and f' (3) by using a graphing device to zoom in on the graph of f . (b) Use symmetry to deduce the values of f ' ( − 1 2 ) , f' (–1), f' (–2), and f' (–3). (c) Use the values from parts (a) and (b) to graph f' (d) Guess a formula for f' ( x ). (e) Use the definition of derivative to prove that your guess in part (d) is correct.
Let f ( x ) = x 3 . (a) Estimate the values of f' (0), f ' ( 1 2 ) , . f' (1), f' (2), and f' (3) by using a graphing device to zoom in on the graph of f . (b) Use symmetry to deduce the values of f ' ( − 1 2 ) , f' (–1), f' (–2), and f' (–3). (c) Use the values from parts (a) and (b) to graph f' (d) Guess a formula for f' ( x ). (e) Use the definition of derivative to prove that your guess in part (d) is correct.
Solution Summary: The author explains how to estimate the value of fprime's value by using an online graphing calculator.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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.