The cost function C ( x ) C(x) C ( x ) and the selling price of each article, p ( x ) p(x) p ( x ) are given below. Determine the profit function P ( x ) P(x) P ( x ) . C ( x ) = − 0.03 x 2 + 70 x + 75 C(x)=-0.03x^2+70x+75 C ( x ) = − 0.03 x 2 + 70 x + 75 p ( x ) = 80 − 0.02 x p(x) = 80 - 0.02x p ( x ) = 80 − 0.02 x

P ( x ) = 0.01 x 2 + 10 x − 75 P(x)=0.01x^2+10x-75 P ( x ) = 0.01 x 2 + 10 x − 75

P ( x ) = 0.01 x 2 − 10 x − 75 P(x)=0.01x^2-10x-75 P ( x ) = 0.01 x 2 − 10 x − 75

P ( x ) = 0.03 x 2 + 10 x − 75 P(x)=0.03x^2+10x-75 P ( x ) = 0.03 x 2 + 10 x − 75

P ( x ) = 0.03 x 2 − 10 x − 75 P(x)=0.03x^2-10x-75 P ( x ) = 0.03 x 2 − 10 x − 75

Tangent Lines and Derivatives

2. Intro to Derivatives / Tangent Lines and Derivatives / Problem 1

Problem 1

The cost function $C(x)$ and the selling price of each article, $p(x)$ are given below. Determine the profit function $P(x)$ .
$C(x)=-0.03x^2+70x+75$
$p(x) = 80 - 0.02x$

$P(x)=0.01x^2+10x-75$

$P(x)=0.01x^2-10x-75$

$P(x)=0.03x^2+10x-75$

$P(x)=0.03x^2-10x-75$