Some problems provide the opportunity for more than one mistake.

The Goal

Find

The Mistakes

Find the mistakes:

1.

(Roll the mouse over the math to see a hint in red)

2.

(Roll the mouse over the math to see a hint in red)

A Correct Solution

(Roll the mouse over the area above to see the corrections in blue)

Explanations

Differentiating the second factor has caused problems here. In the first mistake for some reason the derivative of the second factor was computed to be -2, with the π in the denominator completely ignored. In the second mistake the quotient rule was applied incorrectly (and without need - if the denominator is a constant, pull it out using the constant mutiple rule and differentiate the numerator); parentheses should have been used around the -2 in the numerator, which should therefore have been π(-2) - 0.

The derivative in this example might be more easily handled by using the constant multiple rule to pull the 1/π out in front and multiplying out x(400 - 2x) before differentiating, as follows: