Difference between revisions of "Introduction to Calculus: What is Derivative and Integral"
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derivative = gradient of a tangent = rate of change | derivative = gradient of a tangent = rate of change | ||
Integral = area under the function. | Integral = area under the function. | ||
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==examples== | ==examples== | ||
#What is the derivative at x=5 | #What is the derivative at x=5 | ||
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#What is the Integral from x=6 to x=10 - by the Integral from x=7 to x=10 | #What is the Integral from x=6 to x=10 - by the Integral from x=7 to x=10 | ||
[[File:Screen Shot 2021-08-24 at 9.09.34 PM.png|thumb]] | [[File:Screen Shot 2021-08-24 at 9.09.34 PM.png|thumb]] | ||
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Revision as of 13:36, 14 September 2021
This is a topic ties every things about (functions and graphs) together.
We're mainly concerned with two parts:
- Derivative (Differentiation)
- Integrals (Integration)
Derivative is equal to rate of change. Most of the time we will us to present how one variable changes with another. The derivative is the gradient of a tangent line
But from the beginning we are going to talk about where do you want the derivative, the other way to say is I will give you a point and then tell me what's the derivative or gradient for that point.
From the beginning here is the concepts you need for calculus.
- "what is the derivative at x=n" you can under stand as "what is the gradient when x=n"
- "What is the Integral at x=a to x=b" you can under stand as "what is the area between the function and the x axis from x=a to x=b".
Conclusion (from the beginning )
derivative = gradient of a tangent = rate of change Integral = area under the function.
examples
- What is the derivative at x=5
- What is the derivative at x=9
- What is the derivative at x=2
- What is the Integral from x=1 to x=4
- What is the Integral from x=3 to x=10
- What is the Integral from x=6 to x=10 - by the Integral from x=7 to x=10
