# Estimate the instantaneous rate of change of the function: `f(x) = 3x^(2) + 4x` at (1,7). Please use a non-derivative way of approaching this (ie. limits).

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### 1 Answer

`f(x)=3x^2+4x`

The instantaneous rate of change of the function at `(a,f(a))=(1,7)` is given by:

`f'(a)=lim_(h-gto) (f(a+h)-f(a))/h`

=`lim_(h->o)` `(f(1+h)-f(1))/h`

=`lim_(h->o)` `[3*(1+h)^2+4(1+h)-(7)]/h`

=`lim_(h->o)` `[3+3h^2+6h+4+4h-7]/h`

=`lim_(h->o)` `(3h^2+10h)/h`

=`lim_(h->o)` `(h(3h+10))/h`

=`lim_(h->o)` `(3h+10)`

Substitute` h=0` ,

`=3*0+10`

`=10` `rarr` **answer**.