# How do you find the instantaneous rate of change at a point on a graph?

The instantaneous rate of change at a point is equal to the function's derivative evaluated at that point. In other words, it is equal to the slope of the line tangent to the curve at that point.

For example, let's say we have a function

If we want to know the instantaneous rate of change at the point

And then we evaluate it at the point

So, the instantaneous rate of change, in this case, would be

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the equation of the line normal to # f(x)=sqrt(1/(x+2) # at # x=-1#?
- Using the limit definition, how do you find the derivative of #f(x) = -7x^2 + 4x#?
- If the tangent line to the curve #y = f(x)# at the point where #a = 2# is #y = 4x-5# , find #f(2)# and #f'(2)#? I know #f(2) = 3# but how do I find #f'(2)#?
- How do you find the equation of the line tangent to #y= -x^3+6x^2-5x# at (1,0)?
- How do you find the equations of both lines through point (2,-3) that are tangent to the parabola #y=x^2+x#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7