Find the derivative ƒ′(x) of the given function y = ƒ(x). b. Graph y = ƒ(x) and y = ƒ′(x) side by side using separate sets of coordinate axes, and answer the following questions. c. For what values of x, if any, is ƒ′ positive? Zero? Negative? d. Over what intervals of x-values, if any, does the function y = ƒ(x) increase as x increases? Decrease as x increases? How is this related to what you found in part (c)? 51. y = -x2 52. y = -1/x 53. y = x3/3 54. y = x4/4
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Find the derivative ƒ′(x) of the given function y = ƒ(x).
b. Graph y = ƒ(x) and y = ƒ′(x) side by side using separate sets of coordinate axes, and answer the following questions.
c. For what values of x, if any, is ƒ′ positive? Zero? Negative?
d. Over what intervals of x-values, if any, does the function y = ƒ(x) increase as x increases? Decrease as x increases? How is this related to what you found in part (c)?
51. y = -x2 52. y = -1/x
53. y = x3/3 54. y = x4/4
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 4 images