I need major help asap please!!!! PRE CALC.!!!!?

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

ok here is the solution to the problem:

you have to apply the equation of the secant line which yields the average rate of change for the equation

Ave Rate of Change = f(x+h)-fx / h

this means , every time you see an x in your equation you must substitute (x + h)

so we have

7(x + h )^2 - [ 7x^2-3x+9] times 1/h

foil

7(x^2+2xh+h^2)- 7x^2+3x+9 times 1/h  <--- distributed negative

7x^2+14xh+7h^2-  7x^2 + 3x +9 times 1/h combine like terms

(14x+7h^2)- 3x + 9 times 1/h

factor h out of first term and cancel the 1/h

h(14x+7h)-3x+9 times 1/h

14x + 7h -3x+9

11x+7h+9 = average rate of change also known as secant line.