Home > Calculus > Instantaneous Rate of Change at a Point

How do you find the instantaneous rate of change of #f (x)= x ^2 +2 x ^4# at #x=1#?

Answer 1

Emilia Aguilar

# 10" unit/sec."#

We know that, the Instantaneous Rate of Change of #f# at #x=1#

is given by #f'(1)#.

#f(x)=x^2+2x^4 rArr f'(x)=2x+2(4x^3)#.

#:."The Reqd. Rate"=f'(1)=2+8=10" unit/sec."#

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Answer 2

Ezra Adams

To find the instantaneous rate of change of (f(x) = x^2 + 2x^4) at (x = 1), you need to find the derivative of the function with respect to (x), (f'(x)). Then, evaluate (f'(1)) to get the instantaneous rate of change at (x = 1).

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Answer from HIX Tutor

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.