Calculus Derivatives Q: F(x)= x^4, x subset 0 = 2 and x subset 1 = 3

[empto]

I have been struggling with this Calculus problem and am wondering if someone could help me:
F(x)= x^4, x subset 0 = 2 and x subset 1 = 3
Find the instantaneous rate of change of y with respect to x at the given value of x subset 0.

I've figured out that you need to use the derivative of the function and that f'(x) is 4x, but I'm unsure what the next step is. Thanks!

 

[empto]

Calculus Derivatives Question

I have been struggling with this Calculus problem and am wondering if someone could help me:
F(x)= x^4, x subset 0 = 2 and x subset 1 = 3
Find the instantaneous rate of change of y with respect to x at the given value of x subset 0.

I've figured out that the derivative of the function is needed and that f'(x) is 4x, but I'm unsure what the next step is. Thanks!

 

[Deleted member 4993]

I have been struggling with this Calculus problem and am wondering if someone could help me:
F(x)= x^4, x subset 0 = 2 and x subset 1 = 3
Find the instantaneous rate of change of y with respect to x at the given value of x subset 0.

I've figured out that you need to use the derivative of the function and that f'(x) is 4x, but I'm unsure what the next step is. Thanks!

You started with capital F [writing F(x)] and you are suddenly bringing in f'(x)!! Where did that small f come from?

Assuming you meant F'(x), your calculation of derivative is incorrect.

F(x) = x^4 → F'(x) = 4* x^3

Now tell us what do you know about the "instantaneous rate of change".

How is "instantaneous rate of change" is related to the derivative?

 

[stapel]

F(x)= x^4, x subset 0 = 2 and x subset 1 = 3

Does "subset" here possibly actually mean "subscript", so the above means the following?

. . . . .F(x) = x⁴, with x₀ = 2 and x₁ = 3

If not, kindly please reply with an explanation of your meaning.

Find the instantaneous rate of change of y with respect to x at the given value of x subset 0.

I will assume that "y" here means "F(x)". The "instantaneous rate of change" is, as usual, the derivative at the stated value of the independent variable, x.

I've figured out that the derivative of the function is needed and that f'(x) is 4x...

No. What is the Power Rule for derivatives? Apply that Rule for this derivative.

...but I'm unsure what the next step is.

Do what they tell you. They've told you to find the answer "at the given value", so plug in that value. :wink: