Calculus Examples

$R (x) = 60 x - 0.5 x^{2}$ , $C (x) = 4 x + 15$

Step 1

Set up the composite result function.

$C (R (x))$

Step 2

Evaluate $C (60 x - 0.5 x^{2})$ by substituting in the value of $R$ into $C$ .

$C (60 x - 0.5 x^{2}) = 4 (60 x - 0.5 x^{2}) + 15$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$C (60 x - 0.5 x^{2}) = 4 (60 x) + 4 (- 0.5 x^{2}) + 15$

Step 3.2

Multiply $60$ by $4$ .

$C (60 x - 0.5 x^{2}) = 240 x + 4 (- 0.5 x^{2}) + 15$

Step 3.3

Multiply $- 0.5$ by $4$ .

$C (60 x - 0.5 x^{2}) = 240 x - 2 x^{2} + 15$

Step 4

Reorder $240 x$ and $- 2 x^{2}$ .

$C (60 x - 0.5 x^{2}) = - 2 x^{2} + 240 x + 15$