IF `f(x)=2x^(3)+3x^(2)+5`, then find the value of `f(2)`.

Answer

To find the value of \( f(2) \) for the function \( f(x) = 2x^3 + 3x^2 + 5 \), we will follow these steps:

### Step 1: Substitute \( x \) with \( 2 \)
We start by substituting \( x \) in the function with \( 2 \):
\[ f(2) = 2(2)^3 + 3(2)^2 + 5 \]

### Step 2: Calculate \( (2)^3 \) and \( (2)^2 \)
Next, we calculate the powers of \( 2 \):
\[ (2)^3 = 8 \quad \text{and} \quad (2)^2 = 4 \]

### Step 3: Substitute the calculated values back into the function
Now, we substitute these values back into the equation:
\[ f(2) = 2(8) + 3(4) + 5 \]

### Step 4: Perform the multiplications
Now we perform the multiplications:
\[ f(2) = 16 + 12 + 5 \]

### Step 5: Add the results
Finally, we add the results together:
\[ f(2) = 16 + 12 = 28 \]
\[ f(2) = 28 + 5 = 33 \]

### Conclusion
Thus, the value of \( f(2) \) is:
\[ \boxed{33} \]

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