Question

Given that a function is given as r(q) = 100q - 2q^2, the value of q at which the derivative of with respect to q is zero?

Answer 1

The derivative is given by
r‘(q) = 100 - 2* 2 * q = 100-4q

We get this by simply using the rule for derivatives of polynomials („take down the exponent as a factor and subtract one in the exponent“)

Then r‘(q)=100-4q=0

100=4q
25=q

At q =25 the derivative r‘ is zero