# Polynomials and their Gradient 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

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
Check my answer (3)

What is the connection between the value of a (the x squared coefficient) and the gradient function?

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

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

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 ?

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?

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

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

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

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.