Bradley C. answered • 10/26/20
Tutor with knowledge ranging from Elementary to College-level Math
Let f(x)=2-5x+13x^2. Calculate the following values: f(a)= , f(a+h)= , f(a+h)-f(a)/h= for h can not equal 0
f(a) = 2 - 5*a + 13*a^2 = 13a2 - 5a + 2 (just substitute a for x in the f(x) given)
f(a+h) = 2 - 5(a+h) + 13(a+h)2 (substitute a + h for x in the f(x), similarly to above)
= 2 - 5a - 5h + 13(a2 + 2ah + h2) [distribute -5 * (a + h) and then FOIL (a+h)2]
= 2 - 5a - 5h + 13a2 + 26ah + 13h2 [distribute 13 into (a2 + 2ah + h2), cannot go any further at this
as there are no terms to combine]
[f(a + h) - f(a)] / h = [2 - 5a - 5h + 13a2 + 26ah + 13h2 - (13a2 - 5a + 2)] / h
= [2 - 5a - 5h + 13a2 + 26ah + 13h2 - 13a2 + 5a - 2] / h [distribute - into f(a) expression]
= [-5h + 26ah + 13h2] / h [cancel out factors, there should be 2 of each of 2, 5a, and 13a2]
= -5 + 26a + 13h [divide by h]
