Let f and g be the functions defined by f(t) = 2t2 and g(t) = t3 + 4t. 1) Determine f'(t) and g′(t).
2) Let p(t) = 2t2 (t3 + 4t) and observe that p(t) = f(t) ⋅ g(t). Re-write the formula for p by distributing the 2t2 term. Then, compute p′(t) using the sum and constant multiple rules.
3) p′(t) = f′(t) ⋅ g′(t).
A. True
B. False
4) Let q(t) = t3 + 4t2/2t2 and observe that q(t) = g(t)/f(t). Rewrite the formula for q by dividing each term in the numerator by the denominator and simplify to write q as a sum of constant multiples of powers of t. Then, compute q′(t) using the sum and constant multiple rules.
5) q′(t) = g′(t)/f'(t).
A. True
B. False

1)

2)

3) False

4)

5) False

Step-by-step explanation:

Given that:

and

Formula:

1) Using above formula:

2)

Rewriting the formula by distributing the term:

3) By using answers of part (1):

Therefore it is False that

4)

Writing by distributing:

Using the formula:

(5)By using answers in part (1):

Therefore, it is False that:

you can't solve x because it is 2 linear equation and you only have one equation

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