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

##### 1 Answer
Aug 4, 2018

$10 \text{ unit/sec.}$

#### Explanation:

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

is given by $f ' \left(1\right)$.

$f \left(x\right) = {x}^{2} + 2 {x}^{4} \Rightarrow f ' \left(x\right) = 2 x + 2 \left(4 {x}^{3}\right)$.

$\therefore \text{The Reqd. Rate"=f'(1)=2+8=10" unit/sec.}$