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.

Question

Function: y=(4x+2)^2

Point: (0,4)

Answer 1

Slope is another way to ask the rate of change of y (dependent variable) with x (independent variable).

f(x) = y = (4x + 2)²

f'(x) = dy/dx = 2 * (4x + 2) * 4 (via power rule and chain rule)

at the point (0,4), the value of x will give you the slope the curve...

f'(0) = 8 * (4*0 + 2) = 16