q(p) =
2.5
p
+ 3.2; q'(5)
To find the derivative of the function q(p), you can use the power rule and the constant multiple rule. The power rule states that if you have a term of the form x^n, the derivative is n * x^(n-1). The constant multiple rule states that if you have a term of the form k * f(x), the derivative is k * f'(x), where f'(x) is the derivative of f(x).
First, let's rewrite the function in a simplified form:
q(p) = 2.5p + 3.2
To find q'(5), we need to find the derivative of q(p) and then evaluate it at p = 5.
Using the constant multiple rule, the derivative of 2.5p is simply 2.5. Since the derivative of a constant (in this case 3.2) is zero, the derivative of 3.2 is also zero.
So, the derivative of q(p) is q'(p) = 2.5.
Now, we can evaluate q'(p) at p = 5:
q'(5) = 2.5.
Therefore, q'(5) = 2.5.