Question

"A function is defined by the equation f(x)=3x^2-4x+2.

a. Find the average slope between the points where x=0 and x=4.
b. Find the slope at x=4."

A) 8,20
B)20,8
C)6,20
D) 8,32

Answer 1

a. The average slope between the points where x=0 and x=4 can be found using the formula for slope. b. The slope at x=4 can be found by taking the derivative of the function and evaluating it at x=4.

Step-by-step explanation:

To find the average slope between two points, we need to find the slope of the secant line that passes through the two points. To do this, we use the formula for slope: m = (y2 - y1) / (x2 - x1).

a. For x = 0 and x = 4, we have the points (0, f(0)) and (4, f(4)). Plugging the coordinates into the formula, we get m = (f(4) - f(0)) / (4 - 0). Evaluate f(4) by substituting x = 4 into the function equation, and simplify the expression to find the average slope.

b. To find the slope at x = 4, we can use the derivative of the function. Take the derivative of the function with respect to x and evaluate it at x = 4 to find the slope.