Given f(3)=9 and f(5)=28, using the first two terms of the taylor series, the approximate value of f'(3) is (keep 4 decimal points).

The approximation by Taylor series of f'(3) is 9.5000.

Step-by-step explanation:

Taking the two first terms for Taylor series gives the following expression:

Where e represents the error of the approximation and in this case is of second order. For this particular example, it is no required to calculate.  

Note that in the equation x is the independent variable, in contrast, xo is the value where all the derivatives of the function are calculated and must be defined. Observe that the value for the first derivative in x equal 3 is wanted to know, so xo will be equal 3.

Now to find f'(3) will use the rest of the information that was given:

f(5)=28 (x=5)

Replacing the previous values in the Taylor expansion:

Solving the equation:

There was no rounding in the calculated value.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

mark brainliest

step-by-step explanation:

2 tens + 6 ones

1 ten + 16 ones

0 tens + 26 ones