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For the function
f(x)=x^(2)+2x+4, find the slope of the secant line between
x=1 and
x=4.
Answer:

For the function $f(x)=x^{2}+2 x+4$ , find the slope of the secant line between $x=1$ and $x=4$ . $\newline$ Answer:

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Complex conjugate theorem

Full solution

Q. For the function

f(x)=x^{2}+2 x+4

, find the slope of the secant line between

x=1

and

x=4

.

\newline

Answer:

Calculate $f(1)$ : To find the slope of the secant line between two points on a function, we use the formula for slope, which is the change in $y$ divided by the change in $x$ , or $(f(x_2) - f(x_1)) / (x_2 - x_1)$ . We need to calculate the function values at $x = 1$ and $x = 4$ .
Calculate $f(4)$ : First, calculate $f(1)$ by substituting $x = 1$ into the function $f(x) = x^2 + 2x + 4$ . $\newline$ $f(1) = (1)^2 + 2(1) + 4 = 1 + 2 + 4 = 7$ .
Use slope formula: Next, calculate $f(4)$ by substituting $x = 4$ into the function $f(x) = x^2 + 2x + 4$ . $\newline$ $f(4) = (4)^2 + 2(4) + 4 = 16 + 8 + 4 = 28$ .
Find slope: Now, use the slope formula with $f(1)$ and $f(4)$ to find the slope of the secant line. $\text{Slope} = \frac{f(4) - f(1)}{4 - 1} = \frac{28 - 7}{4 - 1} = \frac{21}{3} = 7.$

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