Please Help me Answer ASAP!! Suppose f′(x) = √(x) sin(x^2) and f(0) = 5. Estimate f(b) for:

Question

Suppose f′(x) = √(x) sin(x²) and f(0) = 5.

Estimate f(b) for:

b = 0 : f(b) ≈ 5

b = 1: f(b) ≈

b = 2 : f(b) ≈

b = 3 : f(b) ≈

Answer 1

Zena

f(1) ≈f(0) + 1. f´(0)

f(2) ≈f(1) + 1. f´(1)

f (3) ≈ f(2) + 1. f´(2)

This is because the linear function starting at x=1 approximating f(x) has slope approximately f´(1).

So just calculate these. You know f(0) and you can find f´(0) putting x=0 into your expression.

That gives you f(1).

Knowing f(1) you can estimate f(2).

Knowing f(2) you can estimate f(3).

Make sure your calculator is set to radian measure when calculating these so you find the sin correctly.

Mike