Find any values where the function is not continuous. Are those values removable or non-removable? f(x)=5/(x-2)
The function is discontinuous at x = 2 because f(2) Does Not Exist. It is a nonremovable discontinuity because it is an asymptote.
Find the point that has a horizontal tangent line for the following function. f(x)=x^2 +4x -5
Horizontal tangent lines occur when the derivative of a function is 0. I will first use the power rule to find f'(x). f'(x) = 2x + 4 I will then substitute zero in for f'(x) and solve. 0 = 2x + 4 -4 = 2x x = -2 To get the y value for the point I will evaluate f(-2) f(-2) = (-2)^2 + 4(-2) -5 = -9 The point (-2,-9) has a horizontal tangent line.
A sporting goods store receives a shipment of 124 basketballs. The shipment includes two types of basketballs, Nike and Wilson. The Wilson balls cost $22.50 each. The Nike balls cost $38.50 each. The bill for the entire shipment was $3,430.00. How many of each type of basketballs were ordered? (Show the system of equations and then solve it!)
x will represent Nike basketballs, y will represent Wilson basketballs. Using the total basketballs you can get the equation x + y = 124 Using the prices of each basketball you can create the equation. 38.5x + 22.5y = 3430 To solve for x and y (the number of each type of basketball) I will use substitution by solving the first equation for y and substituting it into the second equation. y=124 - x 38.5x + 22.5(124 - x) = 3430 I now have one equation with one variable and can solve using opposite operations to get x by itself. 38.5x + 2790 - 22.5x = 3430 16x = 640 x = 40 Nike Basketballs To get y you can substitute 40 back in for x into either original equation y = 124 - 40 y = 84 Wilson Basketballs