If f(x)=3x^2-7x+2, find f'(3).

Question

If f(x)=3x²-7x+2, find f'(3). _____________

Use this to find the linear approximation to f(x) at x = 3.

The equation of this linear approximation is

L(x)= _____________

Use L(x) to approximate f(3.3). (Compute the actual value of L(3.3).)

f(3.3) ≈ _____________

Compare this with the actual value of f(3.3) = _____________

Answer 1

f'(x) =6x - 7; f'(3) = 6·3 - 7 = 11

f(3) = 3·3² - 7·3 + 2 = 8

L(x) = f(3) + f'(3)(x - 3); L(x) = 8 + 11(x - 3) = 11x - 25

f(3.3) ≈ L(3.3) = 11·3.3 - 25 = 11.3