Find f(a),f(a+h) and the difference quotient f(a+h)-f(a) whole divided by h where h is not equal to 0

Question

f(x)=8x^2+1
f(a)
f(a+h)
f(a+h)-f(a)/h

Answer 1

To find f(a), substitute a into the function f(x):

f(a) = 8(a)^2 + 1
= 8a^2 + 1

To find f(a+h), substitute (a+h) into the function f(x):

f(a+h) = 8(a+h)^2 + 1
= 8(a^2 + 2ah + h^2) + 1
= 8a^2 + 16ah + 8h^2 + 1

To find the difference quotient (f(a+h) - f(a)) / h, substitute the expressions found above:

(f(a+h) - f(a)) / h = [(8a^2 + 16ah + 8h^2 + 1) - (8a^2 + 1)] / h
= 16ah + 8h^2 / h
= 16a + 8h