Question

To find the linearization of the function f(x)=x+9 at a=7, Let's find the linearization and then use it to approximate √15.95 and √16.05

Answer 1

To find the linearization of the function f(x)=x+9 at a=7, we find the equation of the tangent line to the graph of f(x) at x=7. Then, we can use this linearization to approximate √15.95 and √16.05.

Step-by-step explanation:

To find the linearization of the function f(x)=x+9 at a=7, we start by finding the equation of the tangent line to the graph of f(x) at x=7.

The slope of the tangent line is equal to the derivative of f(x) at x=7. Since the derivative of f(x)=x is 1 for all values of x, the slope of the tangent line is 1.

The equation of the tangent line is y = 1(x - 7) + (f(7)) = x - 7 + 9 = x + 2.

Now, we can use this linearization to approximate √15.95 and √16.05. Plugging in x=15.95 into the equation y=x+2, we find that y≈17.95. Similarly, plugging in x=16.05, we find that y≈18.05.