Differentiation question!

[Leah5467]

Hello! I don't get the parts here.

1.Why is tangent=the rate of change of the curve? I understand why is it the rate of change but not why is it the change of the curve. Is it some complicated maths that a high school student shouldn't be knowing?

2.Why is function for tangent=function of reverse?





Thank you!

 

[Deleted member 4993]

Hello! I don't get the parts here.

1.Why is tangent=the rate of change of the curve? I understand why is it the rate of change but not why is it the change of the curve. Is it some complicated maths that a high school student shouldn't be knowing?

2.Why is function for tangent=function of reverse?

View attachment 13499
View attachment 13500
View attachment 13501

Thank you!

Do you understand:

The gradient of a tangent at a point [on the graph of y = f(x)] is the rate of change of 'y' with respect to 'x' !

 

[HallsofIvy]

First, the tangent line is NOT the "rate of change" because "rate of change" is a number, not a line. What is true is that the "slope" of the tangent line is the "rate of change". And that slope is the tangent function of the angle the tangent line makes with the x-axis.