Let f( x ) = 2 − 3x + 13x^2. Calculate the following values:

Question

Let f( x ) = 2 − 3x + 13x^2. Calculate the following values:

f (a)=

f(a+h)

f(a+h)−f(a) /h= (For h does not equal 0)

Answer 1

f(x) = 2 - 3x + 13x²

f(a) is simply a change of variables such that

f(a) = 2 - 3a + 13a²

Now,

f(a + h) = 2 - 3(a + h) + 13(a + h)²

f(a + h) = 2 - 3a - 3h + 13a² + 26ah + 13h²

Combining the above results and dividing by h (for h ≠ 0),

(f(a + h) - f(a))/h = (2 - 3a - 3h + 13a² + 26ah + 13h² - 2 + 3a - 13a²)/h

(f(a + h) - f(a))/h = (-3h + 26ah + 13h²)/h

(f(a + h) - f(a))/h = -3 + 26a + 13h

Enjoy Calculus!