A differentiable function f has the property that f(5)=3 and fprime(5)=4. What is the estimate for f(4.8) using the local linear approximation for f at x=5?

Question

anonymous · Answer

The linear approximation means that you assume the function is linear. So just do f(5) +f'(5) (x-5)

anonymous · Answer

This works out, in this specific case to give me:
3 + 4(-0.2)

anonymous · Answer

thanks i understand everything except for the 0.2 part

anonymous · Answer

how do you know to do 4.8 - 5?

anonymous · Answer

For a linear function, I have something like y = mx + b.
m is the CONSTANT slope. If I increase x by some amount, and I want to know how much y has increased, I just multiply m by the increase in x. So, let's say the slope is 2, and x goes from 4 to 7, then x has increased by 3, which means y will have increased by m*x = 2*3 = 6 Now, if x goes from 8 to 7.5, then x has increased by (-0.5), so y will have increased by m * x = 2(-0.5) = -1, which means y went down by 1.

anonymous · Answer

thank you  you so much!

anonymous · Answer

You're welcome =D