for the function f, f(x) = 2x + 1 and f(1) = 4. what is the approximation for f(1.2) found by using the line…

Explanation:

Step1: Recall the tangent line approximation formula

The tangent line approximation formula is (L(x)=f(a)+f^{\prime}(a)(x - a)). Here (a = 1), (x=1.2), (f(x)=2x + 1). First, find the derivative (f^{\prime}(x)). For (y = f(x)=2x + 1), using the power rule ((x^n)^\prime=nx^{n - 1}), we have (f^{\prime}(x)=\frac{d}{dx}(2x+1)=2).

Step2: Evaluate (f(a)) and (f^{\prime}(a))

When (a = 1), (f(1)=2\times1 + 1=3) (but the problem states (f(1) = 4), there might be a mis - statement in the function description. Assuming the function is (y=f(x)) with (f^{\prime}(x) = 2) (derivative of (y = 2x + c) is (2)) and (f(1)=4)).

Step3: Apply the tangent line approximation formula

Substitute (a = 1), (x = 1.2), (f(a)=4), (f^{\prime}(a)=2) into (L(x)=f(a)+f^{\prime}(a)(x - a)). (L(1.2)=f(1)+f^{\prime}(1)(1.2 - 1)) (L(1.2)=4+2\times(1.2 - 1)) (L(1.2)=4+2\times0.2) (L(1.2)=4 + 0.4=4.4)

Answer:

E. (4.4)