function: f(x)=x^2-12x+35
Interval [6,6.5]
How do you find the slope of the second line? Can you show this in the formula? and what would the answer be rounded to four decimal places as needed.
What second line? What first line? That is a parabola. Its slope is
df(x)/dx = 2x - 12
you give an interval. If you want the slope of the line joining two points on the curve for that interval, then as you recall from your long-ago Algebra I, the slope
m = ∆y/∆x = (f(6.5)-f(6))/(6.5-6)
To find the slope of a line, you need two points on the line. In this case, we are given a function, f(x), and the interval [6, 6.5]. We can find the slope of the second line by taking the derivative of the function and evaluating it at any point within the given interval.
First, let's find the derivative of the function f(x):
f'(x) = d/dx (x^2 - 12x + 35)
= 2x - 12
Next, we can evaluate the derivative f'(x) at any value within the given interval [6, 6.5]. Let's choose x = 6.5:
f'(6.5) = 2(6.5) - 12
= 13 - 12
= 1
The slope of the second line is 1. It can be expressed using the formula for a straight line, y = mx + b, where m represents the slope. So, the equation of the second line is y = x + b, where b is the y-intercept.
If you want to round the slope to four decimal places, the answer would be 1.0000.