Basic Differentiation Rules Score 24/30 24/30 answered Question 27 Let g(y)=-4 y2-6+7 y Determine the value(s) of y if any for which g has a horizontal tangent line g has a horizontal tangent line at y= g has no horizontal tangent lines Submit Question

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StudyX AI with GPT-3.5 Turbo Model · Accepted Answer

Solution By Steps
Step 1: Find the derivative of $g(y)$
The derivative of $g(y)$ is found by differentiating each term separately.
$$g'(y) = -8y + 7$$

Step 2: Set the derivative equal to zero
To find where $g$ has a horizontal tangent line, set $g'(y)$ equal to zero and solve for $y$.
$$-8y + 7 = 0$$

Step 3: Solve for $y$
Solve the equation $-8y + 7 = 0$ for $y$.
$$y = \frac{7}{8}$$

Final Answer
$g$ has a horizontal tangent line at $y = \frac{7}{8}$.

Key Concept
Critical Point

Key Concept Explanation
A critical point is where the derivative of a function is zero or undefined. In this case, finding where the derivative is zero helps identify points where the function may have horizontal tangent lines.

Basic Differentiation Rules Score 24 30 24 30 answered Question 27 Let g y 4 y2 6 7 y Determine the value s of y if any for which g has a horizontal tangent line g has a horizontal tangent line at y g...

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Basic Differentiation Rules Score 24 30 24 30 answered Question 27 Let g y 4 y2 6 7 y Determine the value s of y if any for which g has a horizontal tangent line g has a horizontal tangent line at y g...

Question

Solution 1

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