Question

Given the function f(x)=1+5x^2, calculate the following values:

Answer 1

Answer:

$f(a)=1+5a^2$

$f(a+h)=1+5a^2+10ah+5h^2$

$\frac{f(a+h)-f(a)}{h}=10a+5h$

Step-by-step explanation:

We are given $f(x)=1+5x^2$.

Find $f(a)$.  All this means is replace $x$ in $f(x)=1+5x^2$ with $a$.

$f(x)=1+5x^2$

$f(a)=1+5a^2$

Find $f(a+h)$. All this means is replace $(a+h)$ in $f(x)=1+5x^2$ with $(a+h)$.

$f(x)=1+5x^2$

$f(a+h)=1+5(a+h)^2$

$f(a+h)=1+5(a+h)(a+h)$

$f(a+h)=1+5(a^2+2ah+h^2)$

$f(a+h)=1+5a^2+10ah+5h^2$

Find $\frac{f(a+h)-f(a)}{h}$. So we got to put some parts together; the parts above:

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

$\frac{(1+5a^2+10ah+5h^2)-(1+5a^2)}{h}$

Now in the first ( ) I see 1+5a^2 and in the second ( ) I see 1+5a^2, so this means you have (1+5a^2)-(1+5a^2) which equals 0.

$\frac{10ah+5h^2}{h}$

Now assuming h is not 0. we can divide top and bottom by h.

$\frac{10a+5h}{1}$

$10a+5h$