Question

Suppose that f(x) is a function with f(155)=37 and f′(155)=7 .
estimate f(157.5) . f(157.5)=

Answer 1

To estimate f(157.5), we can use the concept of linear approximation by multiplying f'(x) by the change in x. Using the given values, the approximation of f(157.5) is 51.

Step-by-step explanation:

To estimate f(157.5), we can use the concept of linear approximation. Since f'(x) represents the rate of change of f(x) at a particular point, we can approximate the change in f(x) by multiplying f'(x) by the change in x. Therefore, the approximation of f(157.5) is:

f(157.5) ≈ f(155) + f'(155) * (157.5 - 155)

Substituting the given values, we have:

f(157.5) ≈ 37 + 7 * (157.5 - 155)

Simplifying the expression, we get:

f(157.5) ≈ 37 + 14 = 51