Let f(x)=5−1x+12x2. Calculate the following values?

f(x)
= 5 - 1x + 12x²

f(a)
= 5 - 1a + 12a²

f(a + h)
= 5 - 1(a + h) + 12(a + h)²
= 5 - 1a - 1h + 12(a ² + 2ah + h²)
= 5 - 1a - 1h + 12a ² + 24ah + 12h²

[f(a + h) - f(a)] / h
= [(5 - 1a - 1h + 12a ² + 24ah + 12h²) - (5 - 1a + 12a²)] / h
= [5 - 1a - 1h + 12a ² + 24ah + 12h² - 5 + 1a - 12a²] / h

= [-1h + 24ah + 12h²] / h
= [h(-1 + 24a + 12h)] / h
= -1 + 24a + 12h

f(x) = 5 - x + 12x^2

f(a) = 5 - a + 12a^2  Answer//

f(a + h) = 5 - (a + h) + 12(a + h)^2
  = 5 - a - h + 12(a^2 + 2ah + h^2)
= 5 - a - h + 12a^2 + 24ah + 12h^2  
= 12a^2 + 24ah - a + 12h^2 - h + 5 answer//

f(a + h) - f(a)
--------------------
.......h

.12a^2 + 24ah - a + 12h^2 - h + 5 - (5 - a + 12a^2)
=-------------------------------------------------------------------
.................................. h

....12a^2 + 24ah - a + 12h^2 - h + 5 - 5 + a - 12a^2
=--------------------------------------------------------------------
................................. h

....24ah + 12h^2 - h
=---------------------------
............. h

.. h(24a + 12h - 1)
=-------------------------
.............h

= 24a + 12h - 1 answer//

f(a) = 5 -1(a) + 12a²
f(a) = 5 - a + 12a²

f(a+h) = 5 -1(a+h) + 12(a+h)²
f(a+h) = 5 - a - h + 12a² + 24ah + h²

[f(a+h) - f(a)] /h = [(5 - a - h + 12a² + 24ah + h²) - (5 - a + 12a²)]/h
[f(a+h) - f(a)] /h = (5 - a - h + 12a² + 24ah + h² - 5 + a - 12a²)/h
[f(a+h) - f(a)] /h = (-h + 24ah)/h
[f(a+h) - f(a)] /h = h(-1 + 24a)/h
[f(a+h) - f(a)] /h = -1 + 24a