# How do you find the instantaneous rate of change of #g(t)=3t^2+6# at t=4?

Compute the first derivative and evaluate it at

Determine the initial derivative:

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

It depends on what you have in your mathematical toolbox.

If you are using a definition then it depends on the particular definition you are using.

There are several ways to express the definition.

One way of expressing it is to give:

Another is

Still another is

Here is the work for the first definition above.

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

To find the instantaneous rate of change of ( g(t) = 3t^2 + 6 ) at ( t = 4 ), you can calculate the derivative of ( g(t) ) with respect to ( t ) using the power rule, which states that the derivative of ( t^n ) with respect to ( t ) is ( nt^{n-1} ). Applying this rule to ( g(t) ), we get:

[ g'(t) = \frac{d}{dt}(3t^2 + 6) = 6t ]

Next, substitute ( t = 4 ) into the derivative equation:

[ g'(4) = 6(4) = 24 ]

So, the instantaneous rate of change of ( g(t) = 3t^2 + 6 ) at ( t = 4 ) is ( 24 ).

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

- How do you find the slope of a tangent line to the graph of the function# f(x)= -5/x^3# at x=6?
- How do you find the derivative of #(cos x)# using the limit definition?
- What is the first derivative of #x+ tanx# and how do you find the slope of the normal to the curve where #x=pi#?
- How do you find the slope of a tangent line to the graph of the function#2xy^2+xy=y# at y=1?
- How do you find the slope of the tangent line to the graph of the function #h(t)=t^2+3# at (-2,7)?

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