Answer is: option4

4.2

Solution:

We use linear approximation (tangent line approximation) to estimate \( f(2.8) \). The linear approximation formula is:

\[ f(x) \approx f(a) + f'(a)(x - a) \]

where:

• \( a = 3 \),
• \( f(3) = 5 \),
• \( f'(3) = 4 \),
• \( x = 2.8 \).

Apply the linear approximation formula

\[ f(2.8) \approx f(3) + f'(3)(2.8 - 3) \]

Substituting the given values:

\[ f(2.8) \approx 5 + 4(2.8 - 3) \]

Simplify the expression

\[ f(2.8) \approx 5 + 4(-0.2) \] \[ f(2.8) \approx 5 - 0.8 \] \[ f(2.8) \approx 4.2 \]

Final Answer - 4.2