Question
Find the slope of the functio \[ f(x)=x^{2}+1,(-5,26) \] What is the slope of the fun \( m=\square \) (Simplify your ans
Ask by Frazier Huff. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope \( m \) is \(-10\).
Solution
1. First, find the derivative of the function \( f(x)=x^{2}+1 \).
\[
f'(x)=\frac{d}{dx}(x^2+1)=2x
\]
2. Next, substitute \( x=-5 \) into the derivative to obtain the slope at that point.
\[
f'(-5)=2(-5)=-10
\]
Thus, the slope is \( m = -10 \).
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Simplify this solution Beyond the Answer
To find the slope of the function \( f(x) = x^2 + 1 \) at the point (-5, 26), we need to calculate the derivative of the function. The derivative \( f'(x) = 2x \). Now, plug in \( x = -5 \): \[ f'(-5) = 2(-5) = -10 \] So, the slope at the point (-5, 26) is \( m = -10 \). When calculating slopes or derivatives, always verify your derivatives and calculations. A common mistake is using the wrong point for evaluation; ensure the point lies on the curve by substituting \( x \) into the original function. In this case, \( f(-5) = (-5)^2 + 1 = 26 \), confirming that the point is correct. Keep practicing to avoid these slip-ups!
