Question

Determine f(a+h)-f(a)/h for f(x)=1-x^2 and simplify

Answer 1

ANSWER :

The answer is :

$\frac{f(a+h)-f(a)}{h}=-2a-h$

EXPLANATION :

From the problem, we have the function :

$f(x)=1-x^2$

We need to find f(a + h) and f(a).

That will be :

$\begin{gathered} f(a+h)=1-(a+h)^2 \\ =1-a^2-2ah-h^2 \\ \\ f(a)=1-a^2 \end{gathered}$

Then plug in to the required functions :

$\begin{gathered} \frac{f(a+h)-f(a)}{h}=\frac{(1-a^2-2ah-h^2)-(1-a^2)}{h} \\ =\frac{-2ah-h^2}{h} \\ =-2a-h \end{gathered}$