Question

Given that f(x)= x(squared)-3x Evaluate f(2+h)-f(2)/h

Answer 1

Answer: The required value of the given expression is (h +1).

Step-by-step explanation: We are given a function f(x) as follows :

`f(x)=x^2-3x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We are to evaluate the following :

`E=(f(2+h)-f(2))/(h).`

Substituting x = 2 + h in equation (i), we get

`f(2+h)\\\\=(2+h)^2-3(2+h)\\\\=(4+4h+h^2)-6-3h\\\\=4+4h+h^2-6-3h\\\\=h^2+h-2`

and substituting x = 2 in equation (i), we get

`f(2)=2^2-3*2=4-6=-2.`

Therefore, the value of expression E can be evaluated as follows :

`E\\\\\\=(f(2+h)-f(2))/(h)\\\\\\=((h^2+h-2)-(-2))/(h)\\\\\\=(h^2+h-2+2)/(h)\\\\\\=(h^2+h)/(h)\\\\\\=(h(h+1))/(h)\\\\=h+1.`

Thus, the required value of the given expression is (h +1).