What is the instantaneous rate of change of f(x)=3x+5 at x=1?

2 Answers
VNVDVI
Mar 29, 2018

3

Explanation:

"Instantaneous rate of change of f(x) at x=a" means "derivative of f(x) at x=a.

The derivative at a point represents the function's rate of change at that point, or the instantaneous rate of change, often represented by a tangent line with the slope f'(a).

f(x)=3x+5

f'(x)=3, the derivative of a constant is zero, meaning the five plays no role here.

So, at x=1, or at any x actually, the rate of change is 3.

Rohan N.
Mar 29, 2018

3

Explanation:

Rate of change is just the gradient function and the instantaneous rate of change is just the gradient function at a particular point

So to get the gradient function you merely have to differentiate the original function.

f(x)=3

so at f(1)=3 so that is the instantaneous rate of change.

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