Answer: To evaluate f(6), we substitute 6 for x in the expression for f(x):
f(6) = 6(9-6) = 18
To evaluate f(6.1), we substitute 6.1 for x in the expression for f(x):
f(6.1) = 6.1(9-6.1) = 16.99
To approximate f '(6), we can use the formula for the derivative of a function:
f '(x) = lim(h→0) [f(x+h) - f(x)]/h
We can use the values we just calculated to estimate the value of f '(6) by setting x = 6 and h = 0.1:
f '(6) ≈ [f(6.1) - f(6)]/0.1
f '(6) ≈ (16.99 - 18)/0.1
f '(6) ≈ -1.01/0.1
f '(6) ≈ -10.1
Therefore, we can approximate f '(6) as -10.1, rounded to one decimal place.
Explanation: