Consider the function 𝑦=𝑥2−3𝑥+2
y
=
x
2
−
3
x
+
2
.
At what value of 𝑥
x
 is the slope of the tangent line equal to 5
5
?
Select one:
a. −4
−
4
 b. 4
4
 c. 2
2
 d. −2

To solve the problem of finding the value of \(x\) where the slope of the tangent line equals 5 for the function \(y = x^2 - 3x + 2\), we first need to find the derivative of the function. The derivative of the function will give us the slope of the tangent line at any point \(x\).

Given:
\[
y = x^2 - 3x + 2
\]

### Step 1: Differentiate the function.
The derivative of \(y\) with respect to \(x\) is:
\[
\frac{dy}{dx} = 2x - 3
\]

### Step 2: Set the derivative equal to 5.
The slope of the tangent line is given as 5, so we set the derivative equal to 5:
\[
2x - 3 = 5
\]

### Step 3: Solve for \(x\).
Now, solve for \(x\):
\[
2x = 5 + 3
\]
\[
2x = 8
\]
\[
x = 4
\]

Thus, the value of \(x\) at which the slope of the tangent line is equal to 5 is \(x = 4\).

The correct answer is **b. 4**.

Would you like further details or have any other questions? 

Here are 5 related questions:
1. What is the significance of the derivative in finding the slope of the tangent line?
2. How can we graphically interpret the slope of the tangent line for a quadratic function?
3. How does the second derivative of a function help in determining concavity?
4. What happens if the slope is negative? How does that affect the tangent line?
5. Can we use this method to find where the slope is zero?

**Tip:** The derivative of a quadratic function is always linear, meaning the slope changes at a constant rate.

Consider the function y = x^2 − 3x + 2. At what value of x is the slope of the tangent line equal to 5? Select one: a. −4, b. 4, c. 2, d. −2.

Learn how to find the value of x where the slope of the tangent line is 5 for the quadratic function y = x^2 − 3x + 2. This calculus problem involves derivatives and is suitable for students in Grades 10-12.

Math Problem Statement

Consider the function 𝑦=𝑥2−3𝑥+2 y

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