Question

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. Function: f(x) = 8x^2; Point: (2, 2)

a) 16
b) 32
c) 8
d) 4

Answer 1

The slope of the graph of the function at the point (2,2) is 32.

Step-by-step explanation:

To find the slope of the graph at a given point, we need to find the derivative of the function. The function given is f(x) = 8x^2.

To find the derivative, we can use the power rule: d/dx(x^n) = n*x^(n-1). Applying this rule to our function, we have f'(x) = 2*8x^(2-1) = 16x.

To find the slope at the point (2,2), we substitute x = 2 into the derivative: f'(2) = 16(2) = 32. So the slope of the graph at the point (2,2) is 32.