Question

consider the following.
function\tpoint
y = (8x + 1)^2, (0, 1)
find the derivative of the function.
y(x) =
find the slope of the graph of the function at the given point. use the derivative feature of a graphing utility to confirm your results.
y(0) =

Explanation:

Step1: Expand function

\( y = (8x + 1)^2 = 64x^2 + 16x + 1 \)

Step2: Differentiate term by term

\( y'(x) = 128x + 16 \)

Step3: Evaluate derivative at x=0

\( y'(0) = 128(0) + 16 = 16 \)

Answer:

\( y'(x) = 128x + 16 \)
\( y'(0) = 16 \)