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Let's work through part (b) to find the equation of the tangent line at \( x = 5 \).

### Given function:
\[ f(x) = 6x + 8x^2 \]

From part (a), we know the derivative:
\[ f'(x) = 6 + 16x \]

### Step 1: Find the slope of the tangent line at \( x = 5 \)
The slope of the tangent line is the value of the derivative \( f'(x) \) at \( x = 5 \):
\[
f'(5) = 6 + 16(5) = 6 + 80 = 86
\]
So, the slope of the tangent line is \( 86 \).

### Step 2: Find the point on the curve at \( x = 5 \)
To find the point of tangency, we need to calculate \( f(5) \):
\[
f(5) = 6(

Find the equation of the tangent line at x = 5 for the function f(x) = 6x + 8x^2.

Learn how to find the equation of the tangent line at x = 5 for the function f(x) = 6x + 8x^2. This involves using the derivative to find the slope and calculating the point of tangency. A step-by-step solution is provided for high school calculus students.

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