The value of [tex]f(102)[/tex] is approximately 41.
In this question we should use the concepts of secant line and derivative. Derivatives can be estimated by using the following approximation:
[tex]f'(c) = \frac{f(b) -f(a)}{b-a}[/tex], [tex]a\le c \le b[/tex] (1)
Where:
- [tex]f'(c)[/tex] - Derivative at point c.
- [tex]f(a), f(b)[/tex] - Functions evaluated at points a and b.
If we know that [tex]f'(c) = 3[/tex], [tex]a = 100[/tex], [tex]b = 102[/tex] and [tex]f(a) = 35[/tex], then [tex]f(b)[/tex] is:
[tex]f(b) = f(a) + f'(c) \cdot (b-a)[/tex]
[tex]f(b) = 35 + 3\cdot (102-100)[/tex]
[tex]f(b) = 41[/tex]
The value of [tex]f(102)[/tex] is approximately 41.
We kindly invite to see this question on derivatives: https://brainly.com/question/21202620
