Calculus Examples

$f (x) = 4 x - x^{2}$ , $(2, 5)$

Step 1

Evaluate $f (x) = 4 x - x^{2}$ at $x = 2$ .

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Step 1.1

Replace the variable $x$ with $2$ in the expression.

$f (2) = 4 (2) - {(2)}^{2}$

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $4$ by $2$ .

$f (2) = 8 - {(2)}^{2}$

Step 1.2.1.2

Raise $2$ to the power of $2$ .

$f (2) = 8 - 1 \cdot 4$

Step 1.2.1.3

Multiply $- 1$ by $4$ .

$f (2) = 8 - 4$

Step 1.2.2

Subtract $4$ from $8$ .

$f (2) = 4$

Step 1.2.3

The final answer is $4$ .

$4$

Step 2

Since $4$ $\neq$ $5$ , the point is not on the graph.

The point is not on the graph

Step 3