Linear Approximation to Estimate a number

Oct 2019
2
0
The North
I have a couple of online hw questions that have got me stumped. The first states: "Use a linear approximation to estimate the following number" and then provides the number (2.9)^4. the practice problems from the textbook indicate that the answer is simply 2.9^4 which would be 70.7281. This is not accepted.
 
Jun 2019
493
262
USA
Are they looking for something like this, maybe?
$f(x) = x^4$
$\displaystyle f(2.9) = f(3.0 - 0.1) \approx f(3.0) - \left( \frac{df}{dx} \right)_{x=3} \cdot (0.1)$
$\displaystyle = 3^4 - (4\cdot 3^3)\cdot(0.1) = 81.0-10.8 = 70.2$
 
Jun 2019
493
262
USA
Well, the problem is quite ill-defined. Without knowing what the instructor is specifically looking for as far as a, "linear approximation," there's not a whole lot you can do.

I would leave feedback on the problem if possible, including a couple of the methods you used. A good instructor will give you the credit, if possible, and adjust the question for future assignments. A bad instructor, well...