$46$ .) The graph of $f$ includes the point $(2,6)$ and the slope of the tangent line to $f$ at any point $x$ is given by the expression $3 x+4$ . Find $f(-2)$ .

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46

.) The graph of

f

includes the point

(2,6)

and the slope of the tangent line to

f

at any point

x

is given by the expression

3 x+4

. Find

f(-2)

Integrate slope function: To find $f(-2)$ , we need to integrate the given slope function $3x+4$ to get the general form of $f(x)$ . The slope function represents the derivative of $f(x)$ , so we will integrate $3x+4$ with respect to $x$ .
Find general form of $\newline$ $f(x)$ : The integral of $\newline$ $3x$ with respect to $\newline$ $x$ is $\newline$ $(3/2)x^2$ , and the integral of $\newline$ $4$ with respect to $\newline$ $x$ is $\newline$ $4x$ . We also need to add a constant of integration, which we'll call $\newline$ $C$ .
Use point $(2,6)$ to find $C$ : So the general form of $f(x)$ after integration is f(x) = \frac{$3$}{$2$}x^\(2 + $4$ x + C \.
Calculate specific form of (x): We are given that the graph of i includes the point ( $2$ , $6$ ). We can use this information to find the value of the constant C by substituting x= $2$ and f(x)= $6$ into the equation.
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = \left(\frac{3}{2}\right)(2)^2 + 4(2) + C$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = \left(\frac{3}{2}\right)(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = \left(\frac{3}{2}\right)(4) + 8 + C$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ . To find $f(-2)$ , we substitute $f(-2)$ $2$ into the equation $f(-2)$ $0$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ . To find $f(-2)$ , we substitute $f(-2)$ $2$ into the equation $f(-2)$ $0$ . Substituting, we get $f(-2)$ $4$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ . To find $f(-2)$ , we substitute $f(-2)$ $2$ into the equation $f(-2)$ $0$ . Substituting, we get $f(-2)$ $4$ . Simplifying, we get $f(-2)$ $5$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ . To find $f(-2)$ , we substitute $f(-2)$ $2$ into the equation $f(-2)$ $0$ . Substituting, we get $f(-2)$ $4$ . Simplifying, we get $f(-2)$ $5$ . This simplifies to $f(-2)$ $6$ .
Substitute $x=-2$ to find $f(-2)$ : Substituting the values, we get $6 = (\frac{3}{2})(2)^2 + 4(2) + C$ . Simplifying the equation, we get $6 = (\frac{3}{2})(4) + 8 + C$ . This simplifies to $6 = 6 + 8 + C$ . Subtracting $14$ from both sides, we find $C = 6 - 14$ , which gives us $C = -8$ . Now that we have the value of $C$ , we can write the specific form of $f(x)$ as $f(-2)$ $0$ . To find $f(-2)$ , we substitute $f(-2)$ $2$ into the equation $f(-2)$ $0$ . Substituting, we get $f(-2)$ $4$ . Simplifying, we get $f(-2)$ $5$ . This simplifies to $f(-2)$ $6$ . Finally, we find $f(-2)$ $7$ .

464646.) The graph of f f f includes the point (2,6) (2,6) (2,6) and the slope of the tangent line to f f f at any point x x x is given by the expression 3x+4 3 x+4 3x+4. Find f(−2) f(-2) f(−2).

$46$ .) The graph of $f$ includes the point $(2,6)$ and the slope of the tangent line to $f$ at any point $x$ is given by the expression $3 x+4$ . Find $f(-2)$ .