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For the function
f(x)=x^(2)+3, find the slope of the secant line between
x=2 and
x=4.
Answer:

For the function $f(x)=x^{2}+3$ , find the slope of the secant line between $x=2$ and $x=4$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}+3

, find the slope of the secant line between

x=2

and

x=4

.

\newline

Answer:

Average Rate of Change Formula: To find the slope of the secant line between two points on a curve, we use the average rate of change formula, which is the difference in the $y$ -values divided by the difference in the $x$ -values. This is similar to the slope formula for a line, $\frac{y_2 - y_1}{x_2 - x_1}$ .
Find Y-Values: First, we need to find the y-values for $x = 2$ and $x = 4$ by plugging these x-values into the function $f(x) = x^2 + 3$ . For $x = 2$ : $f(2) = (2)^2 + 3 = 4 + 3 = 7$ . For $x = 4$ : $f(4) = (4)^2 + 3 = 16 + 3 = 19$ .
Calculate Slope: Now we have two points on the curve: $(2, 7)$ and $(4, 19)$ . We can use these points to find the slope of the secant line. $\newline$ Slope = $(f(4) - f(2)) / (4 - 2) = (19 - 7) / (4 - 2)$ .
Final Result: Calculate the slope: $(19 - 7) / (4 - 2) = 12 / 2 = 6$ . The slope of the secant line between $x = 2$ and $x = 4$ is $6$ .

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