Higher Order Derivative

Author:: Bed Prasad Dhakal

Topic:: Calculus, Derivative

तलको applet 1 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको चारवटा प्रश्नको उतर दिनुहोस ।

Test Your Understanding 1

What is the value of First derivative at Green points?

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 2

What is the value of First derivative at Blue curve?

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 3

What is the value of First derivative at Red curve?

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 4

Which of the following is true? Check all that apply

Check all that apply

First derivative is positive for increasing curve
First derivative is negative for decreasing curve
First derivative is zero for local maxima/minima
First derivative can be positive, negative or zero for a curve

तलको applet 2 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको चारवटा प्रश्नको उतर दिनुहोस ।

Test Your Understanding 5

What is the value of Second derivative at Green points

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 6

What is the value of Second derivative at Blue curve?

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 7

What is the value of Second derivative at Red curve?

Check all that apply

Positive
Negative
Zero
Constant

Test Your Understanding 8

Which of the following is true? Check all that apply.

Check all that apply

Second derivative is positive for a curve concave upward
Second derivative is negative for a curve concave downward
Second derivative is zero for inflectional point
Second derivative can be positive, negative or zero for a curve

तलको applet 3 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको तिनवटा प्रश्नको उतर दिनुहोस ।

Test your understanding 9

The value of First derivative at Blue curves are

Check all that apply

Increasing
Decreasing
Zero
Constant

Test your understanding 10

What is the value of First derivative at Red curve?

Check all that apply

Increasing
Decreasing
Zero
Constant

Test your understanding 11

Which of the following is true? Check all that apply

Check all that apply

First derivative is increasing for a curve concave upward
First derivative is decreasing for a curve concave downward
First derivative is zero inflectional point
Second derivative is zero at stationary points

Below are three graphs. One of the graphs of f(x), another is f’(x), and another is f’’(x). Identify which is which?

Test your understanding 12

In the figure below, which is true?

Check all that apply

the curve p is f(x), the curve q is f'(x), the curve r is f'(x)
the curve r is f(x), the curve q is f'(x), the curve p is f'(x)
the curve p is f(x), the curve r is f'(x), the curve q is f'(x)
the curve q is f(x), the curve p is f'(x), the curve r is f'(x)

Higher Order Derivative

तलको applet 1 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको चारवटा प्रश्नको उतर दिनुहोस ।

Test Your Understanding 1

Test Your Understanding 2

Test Your Understanding 3

Test Your Understanding 4

तलको applet 2 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको चारवटा प्रश्नको उतर दिनुहोस ।

Test Your Understanding 5

Test Your Understanding 6

Test Your Understanding 7

Test Your Understanding 8

तलको applet 3 मा कालो बिन्दुलाई चलाउनुहोस र यस applet को तल दिएको तिनवटा प्रश्नको उतर दिनुहोस ।

Test your understanding 9

Test your understanding 10

Test your understanding 11

Below are three graphs. One of the graphs of f(x), another is f’(x), and another is f’’(x). Identify which is which?

Test your understanding 12

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