Polynomials and their Gradient Functions

Author:
Nicholas Turner
Topic:
Differential Calculus, Functions
In this activity you are going to investigate the relationship between a function and its gradient function The gradient function links the x-value to the gradient of the function at that point.
Select f and f' for a quadratic function and its gradient function.

What type of function is the gradient function of the quadratic function

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Move the sliders a, b and c to change the coefficients of which ones affect the derivative function.

Select all that apply
  • A
  • B
  • C
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What is the connection between the value of a (the x squared coefficient) and the gradient function?

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What is the connection between b (the coefficient of x in the function) and the gradient function?

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What is the connection between the value of c (the y -intercept of the function) and the gradient function?

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For the next part of the investigation you need to unselect f and f' and select g and g' to get a cubic and its derivative function.

What type of function is the gradient function of the cubic function ?

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Move the sliders a, b, c and d to change the coefficient

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

What is the connection between the value of a and the derivative function?

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What is the connection between the value of b and the gradient function?

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What is the connection between the value of c and the gradient function?

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What is the connection between the value of d and the gradient function?

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For the final part of this investigation unselect g and g' and select h and h' for a quartic function and its gradient function. By moving all the sliders try to find similar rules to the ones you have discovered above.

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