PRE CALC.!!! I NEED HELP ASAP?

Question

For the function g(x)=7x^2-3x+9

A. Express the slope of the secant line in terms of x & h

B. Find mSec for h= 0.5, 0.1, and 0.01 at x=1. What value does m Sec approach as h approaches 0?

C.Find the equation for the secant line at x=1 with h=0.01

She didnt teach us this.. and she put it on the homework thats due in 30 mins.

Please help!!

Answer 1

First of all, you need to calm down and read this.  Don't let other people control your emotions.  Control yourself.  

Second, go to school to learn as much as you can.  Some students go to school and perform, but they never really learn much.  Don't let that happen in your school life.

Third, if you do not think that your teacher is actually teaching you and your classmates, then either speak with your parents or go to the principal's office yourself (as I did in tenth grade) and report this.  

And if you ever have a teacher who teaches you how to do specific problems and only gives you such problems in testing, then your teacher does not believe that students can learn and you should complain.

Let's look at a similar function and address the same three questions.

Let f(x) = x^2 - x + 8.

A.  The slope of the secant line using x and h is equal to the slope of the line connecting (x, f(x)) and (x + h, f(x + h)).  Note:  Your teacher and textbook may be using x - h and that's okay.

mSec = [ f(x + h) - f(x) ] / [(x + h) - x]

= [ ( (x + h)^2 - (x + h) + 8 ) - (x^2 - x + 8) ] / h

= [ (x + h)^2 - x^2 - h ] / h.

B.  With x = 1, we have mSec = [ (1 + h)^2 - 1 - h ] / h

= [ (1 + 2h + h^2) - 1 - h] / h  =  (h^2 + h) / h = h + 1.

At h = 0.5, mSec = 0.5 + 1 = 1.5

At h = 0.1, mSec = 0.1 + 1 = 1.1

As h approaches 0, mSec approaches 0 + 1 = 1

C.  The equation for the secant line at x = 1 and h = 0.01 can be found using the two points on it that are on f(x).  Read the first sentence in A. above and use the formula:

If two points on a straight line are (a, b) and (c, d), then the equation of the straight line is

L(x) - b = [(d - b) / (c - a)] (x - a).