Evaluate each of the following. Show all your calculations.
��� f" (0) �if f(x)���� = 14x^2�� + 3x� − 6
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A particle is projected vertically upwards with velocity of u.after t seconds particle is projected from some point with same velocity.How long does it take for the second particle to meet the first particle?
To evaluate f"(0), we need to find the second derivative of the function f(x) = 14x^2 + 3x - 6 and substitute x = 0 into the equation.
Step 1: Find the first derivative of f(x).
The derivative of f(x) = 14x^2 + 3x - 6 with respect to x is given by:
f'(x) = 28x + 3.
Step 2: Find the second derivative of f(x).
To find the second derivative, we need to differentiate the first derivative with respect to x:
f"(x) = (d/dx)(28x + 3).
Differentiating the first derivative, we get:
f"(x) = 28.
Step 3: Substitute x = 0 into f"(x).
Now that we have the second derivative, we can substitute x = 0 into the equation:
f"(0) = 28.
Therefore, the value of f"(0) is 28.