Answer :
To find the value of the function
[tex]$$
f(x) = 6x^4 - 10x^3 + 40x - 50
$$[/tex]
at [tex]$x = 2$[/tex], we substitute [tex]$2$[/tex] for [tex]$x$[/tex]:
[tex]$$
f(2) = 6(2^4) - 10(2^3) + 40(2) - 50.
$$[/tex]
Now, we calculate each term step by step.
1. Calculate the first term:
[tex]$$
2^4 = 16, \quad \text{so} \quad 6(2^4) = 6 \times 16 = 96.
$$[/tex]
2. Calculate the second term:
[tex]$$
2^3 = 8, \quad \text{so} \quad 10(2^3) = 10 \times 8 = 80.
$$[/tex]
3. Calculate the third term:
[tex]$$
40(2) = 80.
$$[/tex]
4. The fourth term is the constant:
[tex]$$
-50.
$$[/tex]
Now, substitute these computed values back into the expression:
[tex]$$
f(2) = 96 - 80 + 80 - 50.
$$[/tex]
Next, perform the arithmetic step by step:
- First subtract [tex]$80$[/tex] from [tex]$96$[/tex]:
[tex]$$
96 - 80 = 16.
$$[/tex]
- Then add [tex]$80$[/tex] to [tex]$16$[/tex]:
[tex]$$
16 + 80 = 96.
$$[/tex]
- Finally, subtract [tex]$50$[/tex] from [tex]$96$[/tex]:
[tex]$$
96 - 50 = 46.
$$[/tex]
Thus, the value of the function at [tex]$x=2$[/tex] is:
[tex]$$
f(2)=46.
$$[/tex]
Therefore, the correct answer is [tex]$\boxed{46}$[/tex].
[tex]$$
f(x) = 6x^4 - 10x^3 + 40x - 50
$$[/tex]
at [tex]$x = 2$[/tex], we substitute [tex]$2$[/tex] for [tex]$x$[/tex]:
[tex]$$
f(2) = 6(2^4) - 10(2^3) + 40(2) - 50.
$$[/tex]
Now, we calculate each term step by step.
1. Calculate the first term:
[tex]$$
2^4 = 16, \quad \text{so} \quad 6(2^4) = 6 \times 16 = 96.
$$[/tex]
2. Calculate the second term:
[tex]$$
2^3 = 8, \quad \text{so} \quad 10(2^3) = 10 \times 8 = 80.
$$[/tex]
3. Calculate the third term:
[tex]$$
40(2) = 80.
$$[/tex]
4. The fourth term is the constant:
[tex]$$
-50.
$$[/tex]
Now, substitute these computed values back into the expression:
[tex]$$
f(2) = 96 - 80 + 80 - 50.
$$[/tex]
Next, perform the arithmetic step by step:
- First subtract [tex]$80$[/tex] from [tex]$96$[/tex]:
[tex]$$
96 - 80 = 16.
$$[/tex]
- Then add [tex]$80$[/tex] to [tex]$16$[/tex]:
[tex]$$
16 + 80 = 96.
$$[/tex]
- Finally, subtract [tex]$50$[/tex] from [tex]$96$[/tex]:
[tex]$$
96 - 50 = 46.
$$[/tex]
Thus, the value of the function at [tex]$x=2$[/tex] is:
[tex]$$
f(2)=46.
$$[/tex]
Therefore, the correct answer is [tex]$\boxed{46}$[/tex].