Mixing
how to graph the derivatives of certain kinds of piecewise functions
$begingroup$
For questions like these, how can I graph the derivative?
For the first image, the sideways x^3 graph is the original and for the second image the v-shaped thing is the original function. For the second question, what is the v-shaped thing called, is there a name like how there are for absolute value functions, parabolas, circles, etc.? For this second image I understand that the function is decreasing so graph is negative, etc. but why does it have a parabola as the derivative?
Also for that first image, i'm confused because I thought that if a function is decreasing its derivative is below x-axis and if it's increasing then derivative is above x-axis, so for the right part of the sideways $x^3$ graph it is under the x-axis because it is decreasing but why is the derivative increasing?
Any help is appreciated, thank you!
calculus derivatives piecewise-continuity
asked Jan 21 at 10:05
user8290579user8290579
40619
$endgroup$
add a comment |
$begingroup$
For questions like these, how can I graph the derivative?
For the first image, the sideways x^3 graph is the original and for the second image the v-shaped thing is the original function. For the second question, what is the v-shaped thing called, is there a name like how there are for absolute value functions, parabolas, circles, etc.? For this second image I understand that the function is decreasing so graph is negative, etc. but why does it have a parabola as the derivative?
Also for that first image, i'm confused because I thought that if a function is decreasing its derivative is below x-axis and if it's increasing then derivative is above x-axis, so for the right part of the sideways $x^3$ graph it is under the x-axis because it is decreasing but why is the derivative increasing?
Any help is appreciated, thank you!
calculus derivatives piecewise-continuity
asked Jan 21 at 10:05
user8290579user8290579
40619
$endgroup$
add a comment |
$begingroup$
For questions like these, how can I graph the derivative?
For the first image, the sideways x^3 graph is the original and for the second image the v-shaped thing is the original function. For the second question, what is the v-shaped thing called, is there a name like how there are for absolute value functions, parabolas, circles, etc.? For this second image I understand that the function is decreasing so graph is negative, etc. but why does it have a parabola as the derivative?
Also for that first image, i'm confused because I thought that if a function is decreasing its derivative is below x-axis and if it's increasing then derivative is above x-axis, so for the right part of the sideways $x^3$ graph it is under the x-axis because it is decreasing but why is the derivative increasing?
Any help is appreciated, thank you!
calculus derivatives piecewise-continuity
asked Jan 21 at 10:05
user8290579user8290579
40619
$endgroup$
For questions like these, how can I graph the derivative?
For the first image, the sideways x^3 graph is the original and for the second image the v-shaped thing is the original function. For the second question, what is the v-shaped thing called, is there a name like how there are for absolute value functions, parabolas, circles, etc.? For this second image I understand that the function is decreasing so graph is negative, etc. but why does it have a parabola as the derivative?
Also for that first image, i'm confused because I thought that if a function is decreasing its derivative is below x-axis and if it's increasing then derivative is above x-axis, so for the right part of the sideways $x^3$ graph it is under the x-axis because it is decreasing but why is the derivative increasing?
Any help is appreciated, thank you!
calculus derivatives piecewise-continuity
calculus derivatives piecewise-continuity
asked Jan 21 at 10:05
user8290579user8290579
40619
asked Jan 21 at 10:05
user8290579user8290579
40619
asked Jan 21 at 10:05
user8290579user8290579
40619
asked Jan 21 at 10:05
user8290579user8290579
40619
asked Jan 21 at 10:05
user8290579user8290579
40619
40619
add a comment |
add a comment |
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