Find the linear approximation, L(x), to f(x) at x = x₀.

Question

Quizplus · Accepted Answer

To find the linear approximation, we need to use the formula: 
L(x) = f(a) + f'(a)(x-a)
where a is the point of approximation.
In this case, a = F1F1F10=10.
So, we need to first find f(a) and f'(a).
f(10) = 2^10 + 3(10) - 1 = 20479.
f'(x) = 2x + 3
f'(10) = 23
Now, we can plug these values into the formula:
L(x) = 20479 + 23(x-10)
Simplifying, we get:
L(x) = 23x - 1061
Therefore, the linear approximation to f(x) at x = S1U1B0 is L(x) = 23x - 1061.
The only answer choice that matches this expression is B.

Find the Linear Approximation, L(x), to F(x) at X =