ap calculus\n4. let f(x) be a differentiable function with f(-1)= 5 and f(-1)= 2. use the given information…

ap calculus\n4. let f(x) be a differentiable function with f(-1)= 5 and f(-1)= 2. use the given information to find the local linear approximation of f(-0.9).\n(a) 4.9\n(b) 5.1\n(c) 5.2\n(d) 5.3

ap calculus\n4. let f(x) be a differentiable function with f(-1)= 5 and f(-1)= 2. use the given information to find the local linear approximation of f(-0.9).\n(a) 4.9\n(b) 5.1\n(c) 5.2\n(d) 5.3

Answer

Answer:

C. 5.2

Explanation:

Step1: Recall linear - approximation formula

The local linear approximation formula is $L(x)=f(a)+f^{\prime}(a)(x - a)$.

Step2: Identify values of $a$, $x$, $f(a)$ and $f^{\prime}(a)$

Here, $a=-1$, $x = - 0.9$, $f(a)=f(-1)=5$, $f^{\prime}(a)=f^{\prime}(-1)=2$.

Step3: Substitute values into formula

$L(-0.9)=f(-1)+f^{\prime}(-1)(-0.9-(-1))$.

Step4: Simplify the expression

$L(-0.9)=5 + 2\times(-0.9 + 1)=5+2\times0.1=5 + 0.2=5.2$.