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

2 Answers
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#.

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.