Question

Given that f(-0.5)=2 and f'(-0.5)=4, using tangent line approximation you would estimate f(0) to be:
A.4
B.-3
C.0
D.1
E.-2

Answer 1

We can use the tangent line approximation formula:

f(x) ≈ f(a) + f'(a)(x-a)

where a is the point we know information about, which in this case is -0.5, and x is the point we want to estimate, which is 0.

Plugging in the given values, we get:

f(0) ≈ f(-0.5) + f'(-0.5)(0-(-0.5))
f(0) ≈ 2 + 4(0.5)
f(0) ≈ 4

Therefore, the answer is A.4.