Calculus question?

g(x) = 4x^2 - 5x

Evaluate and Simplify:
(g(a + h) - g(a))/h

This is just a substitution of the value given in the bracket into the equation.

g(a + h) means x is now a value call a+h, so you just sub this into the equation here and then simplify.

g(a+h) = 4(a+h)^2 - 5(a+h) = 4a^2 + 4h^2 + 8ah - 5a - 5h

Similarly, g(a) means x is at a value called a, again, sub this into the equation here and then simplify.

g(a) = 4a^2 - 5a

You see, now we have both g(a+h) and g(a), we can just put the result we have and carry on with the calculation.

(g(a + h) - g(a))/h = ((4a^2 + 4h^2 + 8ah - 5a - 5h) - (4a^2 - 5a) )/h

= (4a^2 + 4h^2 + 8ah - 5a - 5h - 4a^2 + 5a)/h

= (4h^2 +8ah - 5h)/h

= 4h + 8a - 5 for h not equal to 0.