For the function given by f(x)=x^2+3x-28 and a=4

Question

find lim h→0 f(a+h)-f(a) / h

Answer 1

Hi,

1- f(x) = x2 + 3x + 28

2- f( a+h) = ( a+h) ^2 + 3( a+h ) - 28 = a^2 +2ah +h^2 + 3a + 3h -28

3- f(a) = a^2 +3a - 28

4- f(a+h) - f(a) = a^2 +2ah +h^2 + 3a + 3h -28 - (a^2 +3a - 28) = 2ah + h^2 +3h = h( 2a + h +3 )

5- [f(a+h) - f(a)] / h = h( 2a + h +3 ) / h = ( 2a + h +3 )

6-Now h approaches to the 0 then we have 2a + 3

Now you can choose any number replace on a such as a = 4

lim[f(a+h) - f(a)] / h = 2(4) +3 = 11

I hope it is useful,

Minoo