Question

Calculus: 1. Suppose that the offocial level of the river, in feet, t hours after the start of the storm is given by the function h(t). River height is measured as a number of feet above or below "flood level"; typically river height is a negative number (indicating the river height is some feet below floor level). Officils determine that h(6) = -9 feet and that h'(6)= 1.8.

A) Construct a libnear function L(t) to estimate the water level of the river for times near t=6, (that is, write the linear appromimation equation for h(t) where a=6).

B) Use this model from part A to estimate h(7)

Answer 1

Not much to explain here, this is what it is:
L(t)=h(6)+(t-6)h'(6)

Answer 2

First two terms of the Taylor series.

Answer 3

thomas9 can you plz help me

Answer 4

What's your question/problem?

Answer 5

so the second derivative is sketched.....it is also known that f(x) is increasing for {xl-1<x<1} and is decreasing elsewhere

Answer 6

f(x) has a local max at x= what?
may have more that one answer

Answer 7

the graph is the second derivative but the question is about the original function

Answer 8

and what would the graph look like

Answer 9

can u see the graph i drew?

Answer 10

yes

Answer 11

ok

Answer 12

What does increasing mean in this case? Does that mean the function is really getting bigger, or is a constant function also increasing here?

Answer 13

Oh, I see how to do this.

Answer 14

getting laarger, i believe

Answer 15

In this picture I sketched what the function generally looks like in each region.