Question

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

a) 51
b) 52
c) 53
d) 54

Answer 1

To estimate f(157.5), we can use linear approximation. Using the equation of the tangent line, we can solve for the unknown value of f(157.5) using the provided information about the function and its derivative.

Step-by-step explanation:

To estimate f(157.5), we can use the information given about the function and its derivative. Since the function and its derivative at x = 155 are provided, we can approximate the value of f(157.5) using linear approximation.

To do this, we'll use the equation of the tangent line at x = 155:

y - f(155) = f'(155)(x - 155)

Plugging in the values, we get:

y - 37 = 7(x - 155)

Next, we substitute x = 157.5 into the equation and solve for y:

y - 37 = 7(157.5 - 155)

y - 37 = 7(2.5)

y - 37 = 17.5

y = 54.5

Therefore, the estimated value of f(157.5) is approximately 54.5.