$$ \text{if }x=2t^2+7\text{ and y}=\text{lint} $$  Compute the second derivative and$$ \text{ t} $$ =1

The problem you presented has some ambiguities, particularly with the term "lint." Let's first clarify what "lint" refers to in the equation $ y = \text{lint} $. I will assume you meant something like a general function of $ t $, or that it was a typo.

For now, let's compute the second derivative of $ x $ with respect to $ t $, as that part is clear. The given expression is:

\[
x = 2t^2 + 7
\]

### Step 1: Compute the first derivative of $ x $ with respect to $ t $
We apply basic differentiation rules:

\[
\frac{dx}{dt} = \frac{d}{dt}(2t^2 + 7)
\]

Differentiating term-by-term:

\[
\frac{dx}{dt} = 2 \cdot 2t + 0 = 4t
\]

### Step 2: Compute the second derivative of $ x $ with respect to $ t $
Now, take the derivative of $ 4t $ with respect to $ t $:

\[
\frac{d^2x}{dt^2} = \frac{d}{dt}(4t) = 4
\]

Thus, the second derivative of $ x $ with respect to $ t $ is:

\[
\frac{d^2x}{dt^2} = 4
\]

### Step 3: Evaluate the second derivative when $ t = 1 $
Since the second derivative is a constant value, substituting $ t = 1 $ doesn't change it:

\[
\frac{d^2x}{dt^2} = 4 \quad \text{at} \quad t = 1
\]

So, the second derivative is 4 at $ t = 1 $.

---

Please clarify what "lint" in the expression $ y = \text{lint} $ refers to, and I will update the solution for $ y $ if necessary. Do you have any other questions or need further details?

### Related Questions:
1. How do you compute the second derivative for trigonometric functions?
2. What is the physical interpretation of the second derivative in motion problems?
3. How would you compute the second derivative for a parametric equation?
4. Can you explain how to differentiate implicit functions?
5. What is the relationship between concavity and the second derivative?

**Tip**: The second derivative is useful in determining whether a function is concave up or down at a particular point.

if x = 2t^2 + 7 and y = lint, compute the second derivative and t = 1

Learn how to compute the second derivative of the quadratic function x = 2t^2 + 7 with respect to t, including step-by-step differentiation and evaluation at t = 1. This problem highlights key calculus concepts in differentiation and is suitable for Grades 11-12.

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