Final answer:
The slope of the secant line from x₁=0 to x₂=4 for the function f(x)=1.1x³-34x²+267x+555 is found by evaluating the function at both x-values and computing the difference quotient. The result is a slope of 148.6.
Step-by-step explanation:
To find the slope of the secant line between two points on the function f(x)=1.1x³-34x²+267x+555, we'll evaluate the function at the two given x-values (x1=0 and x2=4), and then use these values to calculate the slope.
Firstly, we find f(0) and f(4) by substituting the x-values into the function:
- f(0) = 1.1(0)³ - 34(0)² + 267(0) + 555 = 555
- f(4) = 1.1(4)³ - 34(4)² + 267(4) + 555 = 1.1(64) - 34(16) + 1068 + 555
Calculating f(4):
1.1(64) - 34(16) + 1068 + 555 = 70.4 - 544 + 1068 + 555 = 1149.4
Now we have the endpoints of the secant line: (0, 555) and (4, 1149.4).
To find the slope a of the secant line, we use the formula:
a = ∆y / ∆x = (f(4) - f(0)) / (4 - 0) = (1149.4 - 555) / (4 - 0) = 594.4 / 4 = 148.6
The slope of the secant line from x1=0 to x2=4 is 148.6.