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

Answer:[tex]f(a)=1+5a^2[/tex][tex]f(a+h)=1+5a^2+10ah+5h^2[/tex][tex]\frac{f(a+h)-f(a)}{h}=10a+5h[/tex]Step-by-step explanation:We are given [tex]f(x)=1+5x^2[/tex].Find [tex]f(a)[/tex].  All this means is replace [tex]x[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex]a[/tex].[tex]f(x)=1+5x^2[/tex][tex]f(a)=1+5a^2[/tex]Find [tex]f(a+h)[/tex]. All this means is replace [tex](a+h)[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex](a+h)[/tex].[tex]f(x)=1+5x^2[/tex][tex]f(a+h)=1+5(a+h)^2[/tex][tex]f(a+h)=1+5(a+h)(a+h)[/tex][tex]f(a+h)=1+5(a^2+2ah+h^2)[/tex][tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]Find [tex]\frac{f(a+h)-f(a)}{h}[/tex]. So we got to put some parts together; the parts above:[tex]\frac{f(a+h)-f(a)}{h}[/tex][tex]\frac{(1+5a^2+10ah+5h^2)-(1+5a^2)}{h}[/tex]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.[tex]\frac{10ah+5h^2}{h}[/tex]Now assuming h is not 0. we can divide top and bottom by h.[tex]\frac{10a+5h}{1}[/tex][tex]10a+5h[/tex]