Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3], (ii)[1,2], (iii)[1,-1], (iv) [1,1.2], (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)).

Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.

Question

Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3],      (ii)[1,2],      (iii)[1,-1],      (iv) [1,1.2],      (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)).

Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.

anonymous · Answer

use a spread sheet
too tedious to do it by hand

anonymous · Answer

or just use wolfram  and copy and past
the function is $3^x$ right?

anonymous · Answer

yes

anonymous · Answer

and all the intervals have $1$ in them, so it is going to be variations on 
$$\frac{3^x-3}{x-1}$$ for different values of $x$

anonymous · Answer

for $[1,3]$ for example it will be this http://www.wolframalpha.com/input/?i=%283^3-1%29%2F%283-1%29

anonymous · Answer

that one was wrong, sorry

anonymous · Answer

oh, no it wasn't doh

anonymous · Answer

here it is for $[1,1.2]$ http://www.wolframalpha.com/input/?i=%283^%281.2%29-1%29%2F%281.2-1%29