Suppose the profit, π, from selling q items of a product is given by π(q) = 2.65q-1200.
Find the value of π'(100).
Since π(q) is a linear function, π'(q) is a constant
In your case π'(q) = 2.65
so π'(100) = 2.65
To find the value of π'(100), we need to find the derivative of the profit function π(q) with respect to q, and then substitute q = 100 into the derivative.
The profit function is given by π(q) = 2.65q - 1200.
To find the derivative of π(q) with respect to q, we can apply the power rule. The power rule states that for any term of the form aq^n, the derivative with respect to q is n*a*q^(n-1).
In this case, the derivative of 2.65q - 1200 with respect to q is:
dπ/dq = d(2.65q)/dq - d(1200)/dq
Using the power rule, we get:
dπ/dq = 2.65 * d(q)/dq - 0
Since d(q)/dq is equal to 1, the derivative simplifies to:
dπ/dq = 2.65
Now, we can substitute q = 100 into the derivative:
π'(100) = 2.65
Therefore, the value of π'(100) is 2.65.